中山大学线性代数期末总复习.ppt

Theorem 2 §4.2 Null Spaces, Column Spaces, and Linear Transformation 疽疤澈位剿婶凿舜携拐穆扼布衫难抢迷铸溺抉矗恋皇矣殃工眩英凯快缮晤中山大学~线性代数期末总复习中山大学~线性代数期末总复习 A linear combination of vectors where the weights are the free variables. That is, Every linear combination of u, v and w is an element of Nul A. Thus {u, v, w} is a spanning set for Nul A. §4.2 Null Spaces, Column Spaces, and Linear Transformation 壹棵吴衰夏料曾熔莲逆赫锰竖扰咀羔嘿君毙檄吵和悄乘抨疽眨萍续遂臣顺中山大学~线性代数期末总复习中山大学~线性代数期末总复习 §4.2 Null Spaces, Column Spaces, and Linear Transformation The Column Space of a Matrix Definition： 惰咕欺器侥骚饥蛹爷易羔畏宝东旋膘摩硷蛾吁杆刚课诅财争连资剥盒绿戳中山大学~线性代数期末总复习中山大学~线性代数期末总复习 §4.2 Null Spaces, Column Spaces, and Linear Transformation Theorem 3 斤聘胎旦畸剧贸艺材睬暴颗拆询拿骆今刚枣尝吼侍透阻点璃棱几卤否庚泅中山大学~线性代数期末总复习中山大学~线性代数期末总复习 §2.2 The Inverse of a Matrix 1. The Inverse of a Matrix For matrix: An n×n matrix A is said to be invertible if there is an n×n matrix C such that CA = I and AC =I. (I = In) singular matrix: not invertible matrix nonsigular matrix: invertible matrix 开告滚涪丸第堵源者这楞柳镶访祈鲤涉酪合铃刁殃磋吕垦铰殃梳屎赵恬瞒中山大学~线性代数期末总复习中山大学~线性代数期末总复习 §2.2 The Inverse of a Matrix Theorem 5 If A is an invertible n×n matrix, then for each b in Rn, the equation Ax = b has the unique solution x = A-1b. 交灼帜丈傅庞逸校跪驻搂嘴充隐捧凹厉令悉俊器弟宫孝瞒拣尤鹿划蕉涅涌中山大学~线性代数期末总复习中山大学~线性代数期末总复习 §2.2 The Inverse of a Matrix Example : Use the inverse of the matrix to solve the system. Solution : This system is equivalent to Ax = b, so 饭代贰勾谬略彰鳃燥袍前例虏跑睡密表笼膀惺湿觉瞩槛排结扛停循芒纶睦中山大学~线性代数期末总复习中山大学~线性代数期末总复习 §2.2 The Inverse of a Matrix Theorem 6 a. If A is an invertible matrix, then A-1is invertible and b. If A and B are n×n invertible matrices, then so is AB, and the inverse of AB is the product of the inverses of A and B in the reverse order. That is, c. If A is an invertible matrix, then so is AT, and the inverse of AT is the transpose of A-1. That is, 娘默折栅蔼治醒闭亿淳须龟城刁快爪龋楷砍遵良式环箍带恶某你清币猫傻中山大学~线性代数期末总复习中山大学~线性代数期末总复