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MATH227 Quiz 5 (Fall 2006)
For full credit, please show all steps in details! 1. Suppose A is an n n matrix and there exist n n matrices C and D such that CA = In and AD = In . Prove that C = D. Is A invertible? Why? (5 points) Note that C =
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MATH227 Quiz 4 (Fall 2006)
For full credit, please show all steps in details! 1. If T : R2 R2 is a linear transformation that rotates points (about the origin) through - radians, find the standard matrix of T . (5 points) 4 Since cos - 4 T
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MATH227 Quiz 2 (Fall 2006)
For full credit, please show all steps in details! 2 0 Let A = [ a1 a2 a3 ] = -1 8 1 -2 combinations of the columns of A (i.e., W (a) Show that 0 and a2 are in W .
6 10 5 , b = 3 , and W be the set of all li
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MATH227 Quiz 3 (Fall 2006)
For full credit, please show all steps in details! 1. Suppose A is a 4 3 matrix and b is a vector in R3 with the property that Ax = b has a unique solution. What can you say about the reduced row echelon form of A?
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MATH227 Quiz 1 (Fall 2006)
For full credit, please show all steps in details! 1. For the following system of linear equations x1 2x2 + 2x3 x3 + 3x2 + 2x3 - 2x4 = -3 = 0 + 3x4 = 1 + x4 = 5 (2 points)
-2x1
(a) Write down the coefficient matrix