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Unformatted text preview: AD = I p . Explain why the equation A x = b has a solution for every b in R p and then explain what this says about the columns of A . 4. (14 points) Do the columns of the following matrix span R 4 ? Justify your answer. 1 2 1 2 1 2 16 6 13 19 1 11 4 8 136237 5. (14 points) Find the inverse of A = " 6 1 11 2 # and use it to solve AX = " 22 3 1 0 5 # 6. (14 points) Find the general ﬂow pattern of the network shown in the ﬁgure. Assuming that the ﬂows 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 = " 5 3 # into 52 3 and v = " 8 5 # into 1 2 4 (a) Find T (3 u + 5 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
 14 points, Dr. Schurle

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