MATH 2211 Midterm: Exam3210Sample1Ans
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Specify whether the matrix has an inverse without trying to compute the inverse. Row reduce the given matrix to an upper triangular matrix and keep track of the operations you perform: 1 r1 + r2 r2, 1 r1 + r3 r3, 1. Then perform 2 r2 + r4 r4 and r2 r3. As a result, the determinant is -32 which is not 0. Answer x1 = x2 = x3 = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) De ne the linear transformation t : p2 p2 by a. ) Determine whether p(x) = x2 x 2 is in the range of t. T(ax2 + bx + c) = cx2 + bx b. First, we nd the corresponding transformation s : r3 r3. We use the ordered standard basis b = Thus, the corresponding transformation s : r3 r3 de ned by (c, b, a) 7 ( b, b, c). The standard matrix of s is given as.
