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midterm_S06 - Princeton University Department of...

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Princeton University Department of Mathematics Name: Instructor: Class time: MAT 202 – Linear Algebra with Applications MIDTERM – March 15, 2006 You have 1 hour and 30 minutes to complete your work. Please show all work and write neatly. Books, notes, calculators, computers are not permitted on this exam. WRITE OUT AND SIGN THE PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination. for the grading problem points score 1 15 2 15 3 20 4 15 5 15 6 20 total 100
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2 (1) Let T : R 2 R 2 be a linear transformation such that T 2 3 = 1 1 and T 1 2 = 1 - 1 . (a) (8 points) Find the images of the standard basis vectors, T ( -→ e 1 ) and T ( -→ e 2 ) . (b) (7 points) Find the matrix of the composition R T where R : R 2 R 2 is the counterclockwise rotation by 90 o .
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3 (2) Let A = 3 1 3 4 1 0 2 1 0 1 - 3 3 2 0 4 3 . (a) (5 points) Find the reduced row-echelon form of A . (b) (5 points) Find a basis for im A .
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