MATH-205 Midterm: Bates MATH 205 100715wong205exam
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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 - october 7, 2015: consider the following system of linear equations (1) 8x1 3x2 + 10x3 = 3. (a) find the solutions to the system (1), if it is consistent. (b) find the solutions to the homogeneous system. 3: let t : r2 r3 be a linear transformation given by. T (x1, x2) = (3x1 + 2x2, x1 + 3x2, x1 + x2). (a) find all ~x such that t (~x) = ~0. (b) determine whether t is one-to-one. Justify your answer. (c) determine whether t is onto. Justify your answer. (c) write a formula for the linear transformation t : r3 r2 so that t (~x) = b~x for any vector ~x in r3. Math 205a,b linear algebra - prof. p. wong.
