Chapter 1.4 InverseMatrix

We use the following conventions a0 in ar aa a if

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Unformatted text preview: eger and let A be an n × n matrix. We use the following conventions: A0 = In . Ar = AA · · · A. If A is invertible, then A−r = A−1 A−1 · · · A−1 . Outline Identity Matrices Inverse of a Matrix Properties of Matrix Powers Theorem If A is an n × n matrix and r , s ∈ Z, then (assuming A is invertible when necessary): 1 Ar As = Ar +s . 2 (Ar )s = Ars . 3 If A is invertible, then so is A−1 , and (A−1 )−1 = A. 4 If A is invertible, then so is Ar , and (Ar )−1 = A−r . 5 6 If A is invertible and k = 0, then aA is invertible, and 1 (kA)−1 = A−1 . k If A is invertible, then so is AT , and (AT )−1 = (A−1 )T . Proof. Check. Outline Identity Matrices Inverse of a Matrix Examples Example 1 Find A−3 if A= 2 11 12 If p (x ) = 2x 2 − x + 3 and A= find p (A). 11 02...
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This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.

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