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# 1. Let B be the following matrix 0 0 B= 0 a 1 0 0 b 0 1 0 c 0 0 1 d (a) For what values of a (and no restrictions on b, c, d) will B be invertible?

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1. Let B be the following matrix B = 0100 0010 0001 abcd (a) For what values of a (and no restrictions on b,c,d ) will B be invertible? Explain. (b) Find B - 1 when it exists.
2. Suppose { v 1 , v 2 , v 3 , v 4 } is a set of linearly independent vectors in R n . Determine, with proper justiFcation, which of the following sets are linearly independent and which are dependent. (a) S = { v 1 + v 2 , v 2 + v 3 , v 3 + v 4 , v 4 - v 1 } . (b) T = { v 1 + v 2 , v 2 + v 3 , v 3 - v 4 , v 4 - v 1 } . (c) U = { v 1 , v 1 + v 2 , v 1 + v 2 + v 3 , v 1 + v 2 + v 3 + v 4 } .
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