MATH 310 Final: Math 310 Final Exam
Document Summary
This is a version of an old exam, with a couple questions replaced. 1. (a) solve the following system of linear equations, putting your answer in parametric vector form: 2x1 + 2x2 + 2x3 + x4 = 12. = 1 x1 + x2 + 2x3 + x4 = 10 (b) consider the matrix a = . Nd the parametric vector form the the solutions to ax = . 1 (a) what is the determinant of a? (b) if ax = b, use cramer"s rule to nd x2: suppose that a = 1(cid:21)(cid:27) are both bases for r2. (b) write down the change of basis matrices p. 1(cid:21), nd both [v]c and [v]b. (d) suppose that t : r2 r2 is a linear transformation so that t (c1) = b1 + 2b2 and t (c2) = b2. Find [t ]c, the matrix for t relative to c.
