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Math416_HW2_sol

# Math416_HW2_sol - Math 416 Abstract Linear Algebra Fall...

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Math 416 - Abstract Linear Algebra Fall 2011, section E1 Homework 2 solutions Section 1.3 3.1. (1 pt check) a. 1 2 3 4 5 6 1 3 2 = 13 31 . b. 1 2 0 1 2 0 1 3 = 7 3 2 . c. 1 2 0 0 0 1 2 0 0 0 1 2 0 0 0 1 1 2 3 4 = 5 8 11 4 . d. The dimensions don’t match (3 6 = 4). 3.2. Let T : R 2 R 2 denote the transformation in question. Its matrix is A = T ( -→ e 1 ) T ( -→ e 2 ) = 0 1 1 0 . 3.3. (2 pts) a. T x y = x + 2 y 2 x - 5 y 7 y = 1 2 2 - 5 0 7 x y says the matrix of T is A = 1 2 2 - 5 0 7 . c. T (1) = 0, T ( t ) = 1, T ( t 2 ) = 2 t , . . . , T ( t n ) = nt n - 1 . The matrix of T is 0 1 0 . . . 0 0 0 2 . . . 0 0 0 0 . . . 0 . . . . . . . . . . . . . . . 0 0 0 . . . n 0 0 0 . . . 0 . 1

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3.4. (1 pt check) a. 1 0 0 0 1 0 0 0 0 b. 1 0 0 0 1 0 0 0 - 1 c. cos θ - sin θ 0 sin θ cos θ 0 0 0 1 = 3 2 - 1 2 0 1 2 3 2 0 0 0 1 where θ = 30 is the angle of rotation.
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Math416_HW2_sol - Math 416 Abstract Linear Algebra Fall...

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