HE1 - Hour Exam I October 15, 2010 1. Find the inverse of...

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Unformatted text preview: Hour Exam I October 15, 2010 1. Find the inverse of the matrix A = 1- 1 1 2- 1 2 . Solution: For this you just need to compute the reduced row echelon form of ( A I ): 1- 1 1 0 0 1 2 0 1 0- 1 2 0 0 1 1 2 0 1 0 1- 1 1 0 0- 1 2 0 0 1 1 0 2 0 1 0 0 1- 1 1 0 0 0 0 1 1 0 1 1 0 0- 2 1- 2 0 1 0 2 1 0 0 1 1 1 . So A- 1 = - 2 1- 2 2 1 1 1 . 2. Find the solution to x 1 + 2 x 2 + 3 x 3 = 0 2 x 1 + 4 x 2 + 7 x 3 + 2 x 4 = 1 in the form ~x = ~v + s~v 1 + t~v 2 , where s and t are arbitrary real numbers. Solution: Written in augmented matrix form this is 1 2 3 0 | 2 4 7 2 | 1 1 2 3 0 | 0 0 1 2 | 1 1 2 0- 6 | - 3 0 0 1 2 | 1 That means x 1 x 2 x 3 x 4 = - 3- 2 s + 6 t s 1- 2 t t = - 3 1 + s - 2 1 + t 6- 2 1 2 3. Suppose that A is an invertible n n matrix, B...
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HE1 - Hour Exam I October 15, 2010 1. Find the inverse of...

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