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**Unformatted text preview: **Math 331 Midterm 2 practice problems This is a list of practice problems for the first midterm in Math 331 (Wylie). The actual exam will be 10 problems long with each problem worth 10 points. The first problem on the exam will be similar to the first practice problem and will be a true/false with 5 parts. You will not need to show any work on this problem. 1. True of False: (a) If A and B are square matrices then det( A + B ) = det( A ) + det( B ). (b) If A is a 5 × 7 matrix with rank 5 then there is only one solution to A x = . (c) Every basis of R 5 has 5 elements in it. (d) If A , B , and C are nonzero n × n matrices and AB = AC , then B = C . (e) If the columns of B are linearly independent then so are the columns of BA . 2. Determine whether the following functions are linear transformations. If the function is a linear transformation find the standard matrix that represents it and determine whether the linear transformation is one-to-one and whether it is onto. (a) T ( x,y ) = ( x,xy ) (b) T ( x,y,z ) = (2 x + 6 y- z, 3 x- 7 y ) (c) T ( x,y,z ) = ( x + 2 y- 4 z- 6 ,- x + 5 y + 9 ,z ) (d) T : R 2 → R 2 is the rotation of the plane by π 4 in counterclockwise direction....

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