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Unformatted text preview: Solutions to even problems from section 2.2 2. Find the inverse of the matrix bracketleftbigg 3 2 7 4 bracketrightbigg . Solution: Since det bracketleftbigg 3 2 7 4 bracketrightbigg = 3(4) − 7(2) = − 2 we have bracketleftbigg 3 2 7 4 bracketrightbigg 1 = − 1 2 bracketleftbigg 4 − 2 − 7 3 bracketrightbigg = bracketleftbigg − 2 1 7 / 2 − 3 / 2 bracketrightbigg 8. Use matrix algebra to show that if A is invertible and D satisfies AD = I , then D = A 1 . Solution: Since A is invertible we know A 1 exists. Thus we have D = ID = ( A 1 A ) D = A 1 ( AD ) = A 1 I = A 1 . 10. True or false? Justify your answer. a. A product of invertible n × n matrices is invertible, and the inverse of the product is the product of their inverses in the same order. Solution: FALSE. For example, if we let A = bracketleftbigg 1 − 1 bracketrightbigg , and B = bracketleftbigg 1 0 1 1 bracketrightbigg then we have ( AB ) 1 = bracketleftbigg 1 − 1 − 1 bracketrightbigg 1 = bracketleftbigg...
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This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.
 Fall '08
 AXENOVICH
 Algebra

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