Unformatted text preview: b is in the column space of A . (b) Identify geometrically, as clearly as you can, the subset of 3dimensional Euclidean space of R 3 that corresponds to the column space of the matrix A = 22 3 52 4 4 . (6) Find necessary and suﬃcient conditions on the entries u 1 ,u 2 ,u 3 ,u 4 under which the following system of linear equations will have at least one solution over Z 5 = { , 1 , 2 , 3 , 4 } , and give the number of solutions in case the conditions are met. 1 2 1 1 2 1 3 111 2 3 21 x 1 x 2 x 3 x 4 = u 1 u 2 u 3 u 4 (7) Consider the system of linear equations Tx = u , where T = 22 3 52 4 4 , u = 11 1 . (a) Solve Tx = u over Q . (b) Solve Tx = u over Z 2 ....
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 Spring '08
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 Linear Algebra, Algebra, 0 m, Ik, Matrix representation, Dr. Macauley HW

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