, 1,0,3 , r i , ai 12 - , ], a2 = [3,-1,5,2], a3 = [-1,0,2,1] t(g) x = [2,3,-7,3

Question

, 1,0,3 , r i , ai 12 - , ], a2 = [3,-1,5,2], a3 = [-1,0,2,1] t(g) x = [2,3,-7,3], ai = [3, 2,2,4], a,-[-2,0,1,-3], a3-6,1, 2,81 In each of the following cases, determine whether the given vector is in the row space of the given matrix: 9. 3 6 2 *(a) [7,1,18], with 2 10 -4 2 -1 4 (b) [4,0,-3], with 2 1 5 -4 -33 41 2 *(c) [2,2,-3], with-2 3 5 T2 -1 0 5 3] (d) [1,2,5-11, with (d) [1,2,5,-1],with|7-1 5 8 2 -4 1 -31 3 7-3 8 Express the vector [13, -23,60] as a linear combination of the vectors ,11,-4,11], with71-1 2 10. (a) the v 12 30l

Explanation / Answer

Yes , the given vector is in the row space of the given matrix , because we can write (1,2,5,1) as linear combination of row vectors of A.

Let

(1,2,5,1) = a(2,-1,0,3) + b(7,-1,5,8)

solving for a and b, we get

a=-3 and b=1

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