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# 3 - Math 136 Assignment#3 1 Let A be a 3 4 matrix and b be...

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Math 136 Assignment #3 1. Let A be a 3 × 4 matrix, and b be a vector in R 3 . Let A 1 2 0 - 2 = b , and A be row equivalent to the matrix 0 1 5 - 8 0 0 1 - 2 0 3 0 1 . Find all solutions to A x = b . 2. Let v 1 = 1 2 3 , v 2 = - 1 1 - 2 , v 3 = 3 3 8 and v 4 = 2 - 4 1 . (a) Determine whether or not the set S = { v 1 , v 2 , v 3 , v 4 } is linearly independent. (b) Find a subset of S consisting of three linearly independent vectors. 3. Find all values of a for which the vectors 1 - 2 3 , 0 1 1 and 1 2 a - 2 - 1 are linearly dependent. 4. Let f 1 ( x ) = x 2 + 2 x + 3, f 2 ( x ) = x 2 + x + 2, f 3 ( x ) = x 2 + 3 x + 4 and f 4 ( x ) = - x 2 + 1. Write one of these polynomials in terms of the others. 5. Let A = a b c d , and ad - bc = 0. Prove that the columns of A are linearly independent. 6. Let { v 1 , v 2 , v 3 , v 4 } be a linearly independent set of vectors. Determine whether or not the following sets are linearly independent:
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