HW4 - Math 601 HOMEWORK 4 1. For each of the following...

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Unformatted text preview: Math 601 HOMEWORK 4 1. For each of the following matrices 12 1001 12 A= , B = 0 0 , C = 48 0101 21 a) find the null space. b) Find the column space. c) Is the matrix invertible? If so, find its inverse, and check your answer. d) Does the matrix have a left inverse? If so, find it, and check your answer. e) Does the matrix have a right inverse? If so, find it, and check your answer. 2. Construct a matrix which transforms the standard basis vectors e1 , e2 , e3 of R3 into three given vectors v1 , v2 , v3 ∈ R3 . When is this matrix invertible? 3. Describe the linear transformation of the plane R2 which are represented in the standard basis by the matrices A1 = 0 −1 10 −1 0 01 , A2 = , A3 = 01 00 4. Let A be an n × n (square) matrix. a) Show that the null space of A2 contains the nulls pace of A. b) Show that the column space of A2 is contained in the column space of A. 1 ...
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