exam3

# exam3 - MAT 242 A 1 2 1 1. (12) Given that A = 2 0 1 1 -3 4...

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MAT 242 A 1 1. (12) Given that A = 2 1 - 3 4 3 1 4 2 6 4 2 1 - 3 5 - 4 0 0 0 - 1 7 is row-equivalent to R = 1 0 - 2 0 78 / 7 0 1 1 0 61 / 7 0 0 0 1 - 7 0 0 0 0 0 : (a) Find a basis for the row space of A . (b) Find a basis for the column space of A .

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Exam 3 2 2. (12) Find a basis for V , where V is the subspace of R 4 spanned by 1 0 - 1 0 , 0 1 2 3 .
MAT 242 A 3 3. (18) Let A = 1 1 2 1 3 1 and b = 12 12 18 . (a) Which one of these is a least squares solution to the linear system A x = b ? ± 6 3 ² ± 3 8 ² ± 3 9 ² ± 12 12 ² ± 12 18 ² (b) Find the orthogonal projection p of b onto Col( A ). (c) Verify that b - p is orthogonal to Col( A ).

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Exam 3 4 4. (18) Let v 1 = 1 0 - 1 0 , v 2 = 0 1 2 3 , v 3 = 0 1 2 - 1 ,
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## This note was uploaded on 06/30/2008 for the course MAT 242 taught by Professor Kaliszewski during the Fall '02 term at ASU.

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exam3 - MAT 242 A 1 2 1 1. (12) Given that A = 2 0 1 1 -3 4...

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