6.4_bzca5e - Section 6.4 Multiplicative Inverses of Matices...

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Section 6.4 Multiplicative Inverses of Matices and Matrix Equations
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The Multiplicative Identity Matrix
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1 0 The Multiplicative Identity matrix is I= for 2 2 matrices. 0 1 That means that AI=A and IA=A × ÷
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The Multiplicative Inverse of a Matrix
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If a square matrix has a multiplicative inverse, it is said to be invertible or nonsingular. If a square matrix has a multiplicative inverse, the inverse is unique. If a square matrix has no multiplicative inverse, it is called singular.
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Example 2 1 Find the multiplicative inverse of A= 7 4 ÷
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A Quick Method for Finding the Multiplicative Inverse of a 2 x 2 Matrix
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Example Find the multiplicative inverse of A using the Quick Method to find the inverse. 3 2 A= 1 4 - ÷ -
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Example Find the multiplicative inverse of A using the Quick Method. Check your work using your 2 3 calculator. A= 1 5 - ÷
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Show that A does not have an inverse. First by calculations, then use your calculator and see what you get for an answer. 3
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This document was uploaded on 10/26/2011 for the course FKP bmfp at UTEM Chile.

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6.4_bzca5e - Section 6.4 Multiplicative Inverses of Matices...

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