电工程数学复资料
线性代数
1 矩阵初等行变换：1）两行互换2）某行非零常数3）某行K倍加行
2 阶梯型矩阵：1）全0行写面2）首非零元列标行标增增
3 行简化阶梯型矩阵：满足列条件阶梯型矩阵：1）首非零元全12）首非零元列余元素全0：
4 求矩阵A秩：A阶梯型矩阵阶梯型矩阵非零行行数矩阵A秩r(A)
例： 设矩阵求矩阵秩．
解：初等行变换矩阵化阶梯形
知矩阵秩2．
5 求矩阵方程AXB：（A B）(I X)XB
求矩阵A逆矩阵：（A I）（I ）
1 例：设矩阵AB求AB 解矩阵方程AXB
解：（AB）
→→
∴＝
例：设矩阵求：
解：
．
6 n元线性方程组解判定
1）AXb ：r(A b)r(A)时方程组解
r(Ab)≠r(A)时方程组解
AX0：方程组定解
2）求齐次线性方程组AX0基础解系：方程组中未知量分取（k00）(0k0)(00k)形式解量
3）求AX0般解全部解：
求AXb般解全部解：
例：设齐次线性方程组系数矩阵初等行变换
求齐次线性方程组基础解系通解．
解：
般解： （中元）
令
令．
方程组基础解系．
方程组通解：中意常数．
例：2线性方程组全部解
解：（A b）→→→方程组般解常数项视零取
相应齐次方程组基础解系取原方程组特解方程组全部解
X+C
例：取值时线性方程组
解解情况求方程组全部解．
解：方程组增广矩阵化阶梯形
知时方程组解时方程组解
时齐次方程组化
分令齐次方程组基础解系
令非齐次方程组特解
原方程组全部解
（中意常数）
二 概率部分
1假设两事件已知求．
解：
2正态分布X～
P(X>b)1P（X
例：设X～N(29)试求（1）P(X<11)(2)P（5Φ（2）09772Φ（3）09987）
解：P(X<11)Φ()Φ(3)09987
P(53估计区间假设检验：正态分布N（
1）方差已知：统计量U中
置信区间：[假设检验：假设
成立
2）方差未知：统计量T
置信区间：[假设检验： 假设
例： 某车间生产滚珠已知滚珠直径服正态分布．批产品里机取出9测直径均值151mm已知批滚珠直径方差试找出滚珠直径均值置信度095置信区间．
解：已知选取样函数
已知计算
滚珠直径均值置信度095置信区间已知条件置信区间
例：某距离进行4次独立测量数（单位：米）：
1551 1547 1550 1552
计算出已知测量系统误差求该距离置信度095置信区间（测量值服正态分布）．
解：未知
已知计算
该距离置信度095置信区间已知条件置信区间
例：资料分析某厂生产批砖抗断强度X～N(325121)批砖中机抽取9块测抗断强度（单位：kgcm）均值3112问批砖抗断强度否合格（α005μ196）
解：假设Ｈ：μ＝325
已知ｎ＝9＝3112 σ＝11
376>196
认批砖抗断强度合格
例：某钢厂生产批材根标准直径100mm批材进行检验机取出9根测直径均值999mm样标准差s047已知材直径服正态分布问批材质量否合格（检验显著性水α005）
解：假设Hμ100
已知：n9 s047 999
认批材质量合格
请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄After earning his spurs in the kitchens of The Westin The Sheraton Sens on the Bund and a sprinkling of other topnotch venues Simpson Lu fi nally got the chance to become his own boss in November 2010 Sort of The Shanghaiborn chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof house at this Sinan Mansions＇stalwart It’s certainly a responsibility to be the head chef and then to have to manage the rest of the restaurant as well the 31yearold tells Enjoy Shanghai In hotels for example these jobs are strictly demarcated so it’s a great opportunity to learn how a business operates across the board It was a task that management back in sunny California evidently felt he was ready for and a vote of confi dence from a company that to date has opened 250 outlets in 11 countries And for added pressure the Shanghai branch was also CPK’s China debut For sure it was a big step and unlike all their other Asia operations that are franchises they decided to manage it directly to begin with says Simpson Two years ago a private franchisee took over the lease but the links to CPK headquarters are still strong with a mainlandbased ＇brand ambassador’ on hand to ensure the business adheres to its ethos of creating innovative hearthbaked pizzas a slice of PR blurb that Simpson insists lives up to the hype They are very innovative he says The problem with most fast food places is that they use the same sauce on every pizza and just change the toppings Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly The largely local customer base evidently agrees and on Saturday and Sunday at least the place is teeming The kidseatforfree policy at weekends is undoubtedly a big draw as well as is the spacious secondfl oor layout overlooked by a canopy of green from Fuxing Park over the road The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week Still the sta are honest enough to admit that business could be better as good in fact as in CPK’s second outlet in the popular Kerry Parkside shopping mall in Pudong Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened and it hasn’t been easy for any of the tenants here adds Simpson We’re planning a third outlet in the city in 2015 and we will probably choose a shopping mall again because of the better foot traffic The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai Xu Junqian visits the Parisian outpost with sweet treats One thing the centuryold Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food pastries in particular One of the most popular tearooms in Paris Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust Now Angelina has packed up its French ambience efficient service and beautiful comforting desserts and flown them to Shanghai At the flagship dinein and takeout space in Shanghai everything mimics the original tearoom designed from the beginning of the 20th century in Paris the height of Belle Epoque The paintings on the wall for example are exactly the same as the one that depicts the landscape of southern France the hometown of the owner and the small tables are intentional imitations of the ones that Coco Chanel once sat at every afternoon for hot chocolate The famous hot chocolate known as L’Africain is a luxurious mixture of four types of cocoa beans imported from Africa blended in Paris and then shipped to Shanghai It’s sinfully sweet rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped cream on the side makes a light but equally gratifying contrast It is also sold in glass bottles as takeaway The signature MontBlanc chestnut cake consists of three parts the pureed chestnut on top the vanilla cream like stuffing and the meringue as base Get all three layers in one scoop not only for the different textures but also various flavors of sweetness The dessert has maintained its popularity for a century even in a country like France perhaps the world’s most competitive place for desserts A much overlooked pairing is the ParisNew York choux pastry and N226 chocolate flavored tea The choux pastry is a mouthful of airy pecanflavored whipped cream while the tea a blend of black teas from China and Ceylon cocoa and rose petals offers a more subtle fragrance of flowers and chocolate Ordering these two items featuring a muted sweetness makes it easier for you to fit into your little black dress Breakfast brunch lunch and light supper are also served at the tearoom a hub of many cultures and takes in a mix of different styles of French cuisines according to the management team The semicooked foie gras terrine is seductive and deceptive It’s generously served at the size and shape of a toast while the actual brioche toast is baked into a curved slice dipped with fig chutney The flavor however is honest strong smooth and sublime And you don’t actually need the toast for crunchiness This is the season for high teas with dainty cups of fine china and little pastries that appeal to both visual and physical appetites But there is one high tea with a difference and Pauline D Loh finds out just exactly why it is special Earl Grey tea and macarons are all very well for the crucial recuperative break inbetween intensive bouts of holiday season shopping And for those who prefer savory to sweet there is still the selection of classic Chinese snacks called dim sum to satisfy and satiate High tea is a meal to eat with eye and mouth an inbetween indulgence that should be light enough not to spoil dinner but sufficiently robust to take the edge off the hunger that strikes hours after lunch The afternoon tea special at ShangXi at the Four Seasons Hotel Pudong has just the right elements It is a pampering meal with touches of luxury that make the high tea session a treat in itself Whole baby abalones are braised and then topped on a shortcrust pastry shell a sort of Chinese version of the Western volauvent but classier Even classier is the dim sum staple shrimp dumpling or hargow upgraded with the addition of slivers of midnight dark truffles This is a master touch and chef Simon Choi who presides unchallenged at ShangXi has scored a winner again Sweet prawns and aromatic truffles — what’s not to love His masterful craftsmanship is exhibited in yet another pastry — a sweet pastry that is shaped to look like a walnut but which you can put straight into the mouth It crumbles immediately and the slightly sweet nutty morsel is so easy to eat you’ll probably reach straight for another My favorite is the dessert that goes by the name yangzhi ganlu or ambrosia from the gods The hotel calls it chilled mango cream with sago pomelo and bird’s nest – made with ingredients that resonate with every female soul It does taste like ambrosia with the sweetsour fragrance of the mango forming the first layer of taste and sensation and the pomelo sacs and sago pearls providing the tactile contrast The bird’s nest — it’s the ingredient that gilds the lily since it is supposed to nourish and nurture a perfect complexion For those unfamiliar with this exotic ingredient the bird’s nest is not a bundle of twigs but is instead the dried secretion that cave swifts use to build their nest Technically it’s bird saliva but the Chinese believe that it has collagenboosting properties essential to beauty To me it just tastes good adding a slight gelatinous crunch to the back of the teeth There is also a baked mushroom puff pastry that includes the highly prized Matsutake or pine mushroom You also get a choice of teas but I strongly recommend the aged Pu’er from Yunnan province It is a mellow tea that will go perfectly with the rich little nuggets and will warm you up on a cold afternoon Incidentally the general guide is green tea such as Longjing or Dragonwell for the hot season semifermented teas like Wulong or Iron Buddha for autumn and more warming teas like Pu’er for winter The ShangXi afternoon tea costs 228 yuan (37) per person and 388 yuan for the more opule
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线性代数
1 矩阵初等行变换：1）两行互换2）某行非零常数3）某行K倍加行
2 阶梯型矩阵：1）全0行写面2）首非零元列标行标增增
3 行简化阶梯型矩阵：满足列条件阶梯型矩阵：1）首非零元全12）首非零元列余元素全0：
4 求矩阵A秩：A阶梯型矩阵阶梯型矩阵非零行行数矩阵A秩r(A)
例： 设矩阵求矩阵秩．
解：初等行变换矩阵化阶梯形
知矩阵秩2．
5 求矩阵方程AXB：（A B）(I X)XB
求矩阵A逆矩阵：（A I）（I ）
1 例：设矩阵AB求AB 解矩阵方程AXB
解：（AB）
→→
∴＝
例：设矩阵求：
解：
．
6 n元线性方程组解判定
1）AXb ：r(A b)r(A)时方程组解
r(Ab)≠r(A)时方程组解
AX0：方程组定解
2）求齐次线性方程组AX0基础解系：方程组中未知量分取（k00）(0k0)(00k)形式解量
3）求AX0般解全部解：
求AXb般解全部解：
例：设齐次线性方程组系数矩阵初等行变换
求齐次线性方程组基础解系通解．
解：
般解： （中元）
令
令．
方程组基础解系．
方程组通解：中意常数．
例：2线性方程组全部解
解：（A b）→→→方程组般解常数项视零取
相应齐次方程组基础解系取原方程组特解方程组全部解
X+C
例：取值时线性方程组
解解情况求方程组全部解．
解：方程组增广矩阵化阶梯形
知时方程组解时方程组解
时齐次方程组化
分令齐次方程组基础解系
令非齐次方程组特解
原方程组全部解
（中意常数）
二 概率部分
1假设两事件已知求．
解：
2正态分布X～
P(X>b)1P（X
例：设X～N(29)试求（1）P(X<11)(2)P（5
解：P(X<11)Φ()Φ(3)09987
P(5
1）方差已知：统计量U中
置信区间：[假设检验：假设
成立
2）方差未知：统计量T
置信区间：[假设检验： 假设
例： 某车间生产滚珠已知滚珠直径服正态分布．批产品里机取出9测直径均值151mm已知批滚珠直径方差试找出滚珠直径均值置信度095置信区间．
解：已知选取样函数
已知计算
滚珠直径均值置信度095置信区间已知条件置信区间
例：某距离进行4次独立测量数（单位：米）：
1551 1547 1550 1552
计算出已知测量系统误差求该距离置信度095置信区间（测量值服正态分布）．
解：未知
已知计算
该距离置信度095置信区间已知条件置信区间
例：资料分析某厂生产批砖抗断强度X～N(325121)批砖中机抽取9块测抗断强度（单位：kgcm）均值3112问批砖抗断强度否合格（α005μ196）
解：假设Ｈ：μ＝325
已知ｎ＝9＝3112 σ＝11
376>196
认批砖抗断强度合格
例：某钢厂生产批材根标准直径100mm批材进行检验机取出9根测直径均值999mm样标准差s047已知材直径服正态分布问批材质量否合格（检验显著性水α005）
解：假设Hμ100
已知：n9 s047 999
认批材质量合格
请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄After earning his spurs in the kitchens of The Westin The Sheraton Sens on the Bund and a sprinkling of other topnotch venues Simpson Lu fi nally got the chance to become his own boss in November 2010 Sort of The Shanghaiborn chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof house at this Sinan Mansions＇stalwart It’s certainly a responsibility to be the head chef and then to have to manage the rest of the restaurant as well the 31yearold tells Enjoy Shanghai In hotels for example these jobs are strictly demarcated so it’s a great opportunity to learn how a business operates across the board It was a task that management back in sunny California evidently felt he was ready for and a vote of confi dence from a company that to date has opened 250 outlets in 11 countries And for added pressure the Shanghai branch was also CPK’s China debut For sure it was a big step and unlike all their other Asia operations that are franchises they decided to manage it directly to begin with says Simpson Two years ago a private franchisee took over the lease but the links to CPK headquarters are still strong with a mainlandbased ＇brand ambassador’ on hand to ensure the business adheres to its ethos of creating innovative hearthbaked pizzas a slice of PR blurb that Simpson insists lives up to the hype They are very innovative he says The problem with most fast food places is that they use the same sauce on every pizza and just change the toppings Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly The largely local customer base evidently agrees and on Saturday and Sunday at least the place is teeming The kidseatforfree policy at weekends is undoubtedly a big draw as well as is the spacious secondfl oor layout overlooked by a canopy of green from Fuxing Park over the road The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week Still the sta are honest enough to admit that business could be better as good in fact as in CPK’s second outlet in the popular Kerry Parkside shopping mall in Pudong Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened and it hasn’t been easy for any of the tenants here adds Simpson We’re planning a third outlet in the city in 2015 and we will probably choose a shopping mall again because of the better foot traffic The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai Xu Junqian visits the Parisian outpost with sweet treats One thing the centuryold Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food pastries in particular One of the most popular tearooms in Paris Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust Now Angelina has packed up its French ambience efficient service and beautiful comforting desserts and flown them to Shanghai At the flagship dinein and takeout space in Shanghai everything mimics the original tearoom designed from the beginning of the 20th century in Paris the height of Belle Epoque The paintings on the wall for example are exactly the same as the one that depicts the landscape of southern France the hometown of the owner and the small tables are intentional imitations of the ones that Coco Chanel once sat at every afternoon for hot chocolate The famous hot chocolate known as L’Africain is a luxurious mixture of four types of cocoa beans imported from Africa blended in Paris and then shipped to Shanghai It’s sinfully sweet rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped cream on the side makes a light but equally gratifying contrast It is also sold in glass bottles as takeaway The signature MontBlanc chestnut cake consists of three parts the pureed chestnut on top the vanilla cream like stuffing and the meringue as base Get all three layers in one scoop not only for the different textures but also various flavors of sweetness The dessert has maintained its popularity for a century even in a country like France perhaps the world’s most competitive place for desserts A much overlooked pairing is the ParisNew York choux pastry and N226 chocolate flavored tea The choux pastry is a mouthful of airy pecanflavored whipped cream while the tea a blend of black teas from China and Ceylon cocoa and rose petals offers a more subtle fragrance of flowers and chocolate Ordering these two items featuring a muted sweetness makes it easier for you to fit into your little black dress Breakfast brunch lunch and light supper are also served at the tearoom a hub of many cultures and takes in a mix of different styles of French cuisines according to the management team The semicooked foie gras terrine is seductive and deceptive It’s generously served at the size and shape of a toast while the actual brioche toast is baked into a curved slice dipped with fig chutney The flavor however is honest strong smooth and sublime And you don’t actually need the toast for crunchiness This is the season for high teas with dainty cups of fine china and little pastries that appeal to both visual and physical appetites But there is one high tea with a difference and Pauline D Loh finds out just exactly why it is special Earl Grey tea and macarons are all very well for the crucial recuperative break inbetween intensive bouts of holiday season shopping And for those who prefer savory to sweet there is still the selection of classic Chinese snacks called dim sum to satisfy and satiate High tea is a meal to eat with eye and mouth an inbetween indulgence that should be light enough not to spoil dinner but sufficiently robust to take the edge off the hunger that strikes hours after lunch The afternoon tea special at ShangXi at the Four Seasons Hotel Pudong has just the right elements It is a pampering meal with touches of luxury that make the high tea session a treat in itself Whole baby abalones are braised and then topped on a shortcrust pastry shell a sort of Chinese version of the Western volauvent but classier Even classier is the dim sum staple shrimp dumpling or hargow upgraded with the addition of slivers of midnight dark truffles This is a master touch and chef Simon Choi who presides unchallenged at ShangXi has scored a winner again Sweet prawns and aromatic truffles — what’s not to love His masterful craftsmanship is exhibited in yet another pastry — a sweet pastry that is shaped to look like a walnut but which you can put straight into the mouth It crumbles immediately and the slightly sweet nutty morsel is so easy to eat you’ll probably reach straight for another My favorite is the dessert that goes by the name yangzhi ganlu or ambrosia from the gods The hotel calls it chilled mango cream with sago pomelo and bird’s nest – made with ingredients that resonate with every female soul It does taste like ambrosia with the sweetsour fragrance of the mango forming the first layer of taste and sensation and the pomelo sacs and sago pearls providing the tactile contrast The bird’s nest — it’s the ingredient that gilds the lily since it is supposed to nourish and nurture a perfect complexion For those unfamiliar with this exotic ingredient the bird’s nest is not a bundle of twigs but is instead the dried secretion that cave swifts use to build their nest Technically it’s bird saliva but the Chinese believe that it has collagenboosting properties essential to beauty To me it just tastes good adding a slight gelatinous crunch to the back of the teeth There is also a baked mushroom puff pastry that includes the highly prized Matsutake or pine mushroom You also get a choice of teas but I strongly recommend the aged Pu’er from Yunnan province It is a mellow tea that will go perfectly with the rich little nuggets and will warm you up on a cold afternoon Incidentally the general guide is green tea such as Longjing or Dragonwell for the hot season semifermented teas like Wulong or Iron Buddha for autumn and more warming teas like Pu’er for winter The ShangXi afternoon tea costs 228 yuan (37) per person and 388 yuan for the more opule
文档香网(httpswwwxiangdangnet)户传
《香当网》用户分享的内容，不代表《香当网》观点或立场，请自行判断内容的真实性和可靠性！
该内容是文档的文本内容，更好的格式请下载文档