lecture10hout

lecture10hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 10) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 11 Outline 1 Inverse of a Matrix 2 A General Method for Finding Inverse Albert Ku (HKUST) MATH 006 2 / 11 Inverse of a Matrix Identity Matrix Definition The identity matrix of order n is given by the following n × n matrix: 1 0 ··· 0 1 ··· 0 0 ··· 0 0 ··· 1 We denote the identity matrix by I . Notice that IM = MI = M for any square matrix M In general, if I is the identity of order n , then IM = M and NI = N where M is an n × m matrix and N is a p × n matrix. Albert Ku (HKUST) MATH 006 3 / 11 Inverse of a Matrix Inverse of a Matrix Definition Let M be a square matrix of order n (i.e., n × n matrix) and I be the identity matrix of order n . If there exists a matrix M- 1 such that M- 1 M = MM- 1 = I , then M- 1 is called the inverse of M ....
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lecture10hout - MATH 006 Calculus and Linear Algebra...

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