Math 220 Sections 8 17 Quiz 4 Due on December 1 2009 in class Show your work for all problems 1 Suppose A and B are 2 2 matrices such that det A a and det B b What is the value of 2 det 3AT B 1 a 9a2 b b 3a2 b c 81a2 b d 3a2 b 9 14 3 4 1 Find the third column of A 1 2 Consider A 2 3 4 1 0 a 1 2 2 1 b 0 3 1 c 3 2 4 d A is not invertible 1 1 3 Find the coordinate vector of x 1 with respect to the basis B v1 v2 v3 where v1 1 1 0 2 1 v2 4 and v3 2 0 1 1 a 1 1 1 b 2 1 0 c 0 1 2 3 d 3 2 1 MATH 220 QUIZ 4 a 4 If det b c 5 1 2 6 5 3 5 then det 3a 7 6 1 2 3b 3c equals 3 7 a 15 b 15 c 5 3 d 5 3 1 0 5 Find the characteristic equation of A 3 4 1 0 1 1 2 a 1 4 2 b 4 2 3 c 4 2 3 d 1 4 3 2 6 Let A 1 1 5 a D 0 0 1 b D 0 0 5 c D 0 0 2 1 3 1 Which of the following matrices is similar to A 2 2 0 0 1 0 0 5 0 0 1 0 0 5 0 0 1 0 0 3 d None of the above 7 Suppose the nullspace of a 3 4 matrix A is a line What is the rank of A a 1 b 2 c 3 d 4 PAGE 2 MATH 220 QUIZ 4 1 2 8 Let A Find A22 0 1 a A 1 0 b 0 1 1 2 c 1 1 1 0 d 2 1 1 1 9 Let A 0 1 1 2 2 1 what is the dimension of the eigenspace corresponding to 0 3 a 0 b 1 c 2 d 3 10 Which of the following is a subspace of R3 a The column space of a 4 3 matrix A b The null space of a 3 4 matrix A c The column space of a 3 4 matrix d None of the above PAGE 3
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