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LinAlgPracticeExam2Spr2008

LinAlgPracticeExam2Spr2008 - Name Linear Algebra Practice...

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Name:__________________ Linear Algebra; Practice Exam 2; Spring, 2008 Show all your work if you want partial credit. 1. Given that . 8 4 7 3 6 2 5 1 B , 0 1 4 2 4 3 1 2 A = - - = Compute (if possible) each of the following: (a) AB (b) BA (c) B T A (d) (AB) T (e) A − B T (f) 2A+B T 2. Consider both parts of this problem. (a) Let T: 2 R 2 R be a linear transformation. Suppose T maps u into ' u and v into ' v where . 7 3 ' , 1 4 , 5 2 ' , 3 1 - = - = - = - = v v u u Use this information to compute T(3 u + v ). (b) How many rows and columns must a matrix A have in order to define a linear transformation from 41 R to 13 R by the rule T( x ) = A x ? 3. Suppose that A is an n × n matrix. Fill in the blanks so that the following statements are logically equivalent. (a) A is invertible. (b) A x = 0 has only the ________ solution. (c) The linear transformation x x A a is ___________.
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