2003sol1 - M346 First Midterm Exam, September 18, 2003 The...

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Unformatted text preview: M346 First Midterm Exam, September 18, 2003 The exam is closed book, but you may have a single hand-written 8 . 5 11 crib sheet. There are 5 problems, each worth 20 points. The first four are calculational, and you MUST JUSTIFY YOUR ANSWERS. Part credit will be given, but answers without justification will not receive credit. The fifth problem is a series of true/false questions. For these, you do not have to show your work, and part credit will NOT be given. 1. Let M 2 , 2 be the space of 2 2 real matrices, with standard basis E = { 1 , 1 , 1 , 1 } and alternate basis B = { 1 2 3 4 , 1 2 3 , 1 4 , 1 } . Let A = 3 2 7 2 . Compute a) the change-of-basis matrix P EB , P EB = [ b 1 ] E [ b 2 ] E [ b 3 ] E [ b 4 ] E = 1 2 1 3 2 1 4 3 4 1 b) the change-of-basis matrix P BE , P BE = P- 1 EB = 1- 2 1 1- 2 1- 2 5- 4 1 c) the coordinates of A in the E basis, and By inspection, [ A ] E = (3...
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2003sol1 - M346 First Midterm Exam, September 18, 2003 The...

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