assign4 - Math 136 Assignment 4 Due: Wednesday, Feb 3rd 3 2...

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Unformatted text preview: Math 136 Assignment 4 Due: Wednesday, Feb 3rd 3 2 −1 2 1 0 −1 0 1 0 , C = 1 . 1. Let A = ,B= 2 1 −2 13 3 −2 a) AB b) BA c) AC d) B T C Determine the following products or state that they are undefined. e) C T C f) BAT 2. If AB is a 2 × 4 matrix, then what size are the matrices A and B ? 3. Determine which of the following sets are linearly independent. b) T = {(1, 1, 0, 1, 1), (2, 3, 1, 3, 3), (0, 1, 1, 1, 1)}. 4. Let S = {x1 , . . . , x } be a set of vectors in Rn . ≤ n. a) S = {(1, −2, 1, 1), (2, −3, 3, 4), (3, −6, 4, 5)}. a) Prove that if S is linearly independent, then b) Consider the following statement “If ≤ n, then S is linearly independent”. Give a proof if the statement is true or a counter example if the statement is false. 5. Prove that if the columns of B are linearly dependent, then so are the columns of AB . 1 ...
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