psLinAlgebra3Qu - Fall 2007 Problem Set #08 Third Lin...

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Fall 2007 ARE211 Problem Set #08 Third Lin Algebra Problem Set Problem 1 Let A = 3 3 - 1 0 - 2 - 3 1 0 - 6 - 2 1 0 0 0 0 1 and B = - 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 - 6 a) Show that A and B are nonsingular. b) Calculate A - 1 , B - 1 , ( AB ) - 1 , and ( A T ) - 1 . c) Solve the linear equation system Ax = 1 - 1 0 0 and ( AB ) x = 1 1 0 0 1
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2 Problem 2 Problem 3 Show that if the matrix A is nonsingular and symmetric, then the matrix A - 1 is also symmetric. (You can use as a fact that the left- and right inverse of the matrix A are the same and that the inverse is unique). Problem 4
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psLinAlgebra3Qu - Fall 2007 Problem Set #08 Third Lin...

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