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Unformatted text preview: the columns of A . 4. (14 points) Are the columns of the following matrix linearly independent? Justify your answer. 1 2 1 2 24 14 1 17 10106 5. (14 points) Find the inverse of A = " 3 8 4 11 # and use it to solve AX = " 1 3 4 21 0 # 6. (14 points) Find the general ow pattern of the network shown in the gure. Assuming that the ows are all nonnegative, what is the largest possible value for x 3 ? 7. (14 points) Suppose the linear transformation T from R 2 to R 3 maps u = " 2 3 # into 3 2 1 and v = " 3 5 # into 6 1 8 (a) Find T (2 u + 3 v ) (b) Show that Span { u , v } = R 2 . (c) Use parametric vector form to describe the range of T ....
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 Spring '09
 KOCH

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