3. The following questions refer to the matrix A below, and the row-reduced form

Question

3. The following questions refer to the matrix A below, and the row-reduced form of A, which appears to the right of A. The vectors ui, U2,,, refer to the columns of the original matrix A. For example v, is the column vector [- 14 3 3 3]. The row-reduced form of A is the matrix M. The vectors , i2, n3,n4,n5 refer to the columns of M. 102-1 01 0 1 4 3 0 -2 5 16 17 01 M=rref(A) =1000 1 0 2-16 -1 3 10 10 2 A= 0 1 (c) find a linear dependence relation among the vectors ai, a2, and a (d) true or false: span[a , a2, a spanfm , m2, ma) (e) true or false: the linear dependence relations among ai, a2, and a are identical to the linear dependence relations among mi, m2, and m.

Explanation / Answer

c) a1-3a2+a4=0

   Since ,(1,0,0,0)-3(0,1,0,0)+(-1,3,0,0)=0

Hence ,the linear dependency relation among a1,a2,a3 is a1+a4=322

d)True ,the span of m1,m2,m3 is same as span ofa1,a2,a3

e)True, the dependency relations among a1,a2,a3 is similar to dependency relations among m1,m2,m3 they only differ by constant.

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