MATH-205 Midterm: Bates MATH 205 020613wong205exam
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Explain all your work and give reasons to support your answers. Advice: don"t spend too much time on a single problem. Exam i - february 6, 2013: (a) let t : r2 r3 be a transformation given by. T (x, y) = (x y, 2x + y, x). Show that t is a linear transformation. (b) let w : r2 r3 be a linear transformation such that w "1. 2# and " 2 and w " 2. 3: consider the following system of linear equations (1) = 0. (a) find one particular solution to the system (1). (b) find the general solutions to the homogeneous system. = 0. (c) find the general solutions to the non-homogeneous system (1). Exam i - february 6, 2013: let s : r2 r2 be a linear transformation given by. S(x1, x2) = (3x1 + 5x2, x1 2x2). (a) find all ~x such that s(~x) = ~0. (b) determine whether s is one-to-one.
