Chapter 1.4 InverseMatrix

Example demonstrate the theorem for 2 4 matrices a

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Unformatted text preview: Example Demonstrate the theorem for 2 × 4 matrices: A= a11 a12 a13 a14 a21 a22 a23 a24 Theorem If A is an n × n matrix and R is the row-reduced echelon form of A, then either R contains a row of zeros or R = In . Outline Identity Matrices The Inverse of a Matrix Definition Let A be an n × n matrix. 1 An n × n matrix B satisfying AB = In and BA = In is called an inverse of A. 2 If A has an inverse, we say that A is invertible. 3 If A is not invertible, we say A is singular. Inverse of a Matrix Outline Identity Matrices Inverse of a Matrix Examples Example 1 Show that B is an inverse of A, where A= 2 1 −2 −3 5 and B = Show that the matrix: 123 A= 4 5 6 000 is singular. −5 −2 −3 −1 Outline Identity Matrices Inverse of a Matrix Uniqueness of Inverses Theorem If A is an n × n matrix, and both B and C are inverses of A, then B = C ....
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