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Unformatted text preview: R 3 ? Show your work and explain your answer. 113 , 5 6 8 , 1 1 h 5. (a) (6 points) Let A be a 7 × 4 matrix. What must a and b be in order to deﬁne a linear transformation T : R a → R b by T ( x ) = A x ? (b) (8 points) Let T : R 2 → R 2 be a linear transformation for which T " 1 #! = " 2 3 # and T " 1 #! = " 52 # . Find T "1 3 #! . 6. Let A = " 3 2 1 1 # and B = "2 1 11 # . Compute or ﬁnd or answer the following. (a) (3 points) 3 A + 2 B (b) (3 points) A T B T (c) (3 points) AB (d) (5 points) The fourth column of AC , where C is a 2 × 9 matrix whose fourth column is " 1 1 # . (e) (6 points) Is there a 2 × 2 matrix D whose entries are not all zero for which AD = " 0 0 0 0 # ? Explain your answer....
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 Fall '08
 PAVLOVIC
 augmented matrix, Dr. Schurle, M340L EXAM 1A

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