Math 220, Sections 8 & 17 - Quiz #4Due on December 1, 2009, in class.Show your work for all problems1. Suppose A and B are 2 × 2 matrices such that det A = a and det B = b. What is the value ofdet3AT2B−1.a) 9a2/bb) 3a2/bc) 81a2/bd) 3a2b2. Consider A =9 −14 3−2 4 −13 −4 1. Find the third column of A−1.a)0−1/2−2b)10−3c)13/24d) A is not invertible.3. Find the coordinate vector of x =1−11with respect to the basis B = {v1, v2, v3}, where v1=110,v2=240, and v3=121.a)1−11b)1−21c)001/2d)3−3/21MATH 220 QUIZ 4 PAGE 24. If deta 5 6b 1 3c 2 7= 5, then det5 1 23a 3b 3c6 3 7equalsa) 15b) −15c) 5/3d) −5/35. Find the characteristic equation of A =−1 0 1−3 4 11 0 2a) (−1 − λ)(4 − λ)(2 − λ)b) 4(λ2− λ − 3)c) (4 − λ)(λ2− λ − 3)d) (−1 − λ)(4 − λ)(3 − λ)6. Let A =2 2 11 3 11 2 2. Which of the following matrices is similar to A?a) D =5 0 00 1 00 0 5b) D =1 0 00 1 00 0 5c) D =5 0 00 1 00 0 3d) None of the above.7. Suppose the nullspace of a 3 × 4 matrix A is a line. What is the rank of A?a) 1b) 2c) 3d) 4MATH 220 QUIZ 4 PAGE 38. Let A =1 −20 −1. Find A22a) Ab)1 00 1c)1 2−1 1d)1 0−2 19. Let A =1 1 20 1 11 2 3, what is the dimension of the eigenspace corresponding to λ = 0a) 0b) 1c) 2d) 310. Which of the following is a subspace of R3?a) The column space of a 4 × 3 matrix Ab) The null space of a 3 × 4 matrix Ac) The column space of a 3 × 4 matrixd) None of the
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