Question

Find the matrix X so that

Answer 1

Given matrix relation is,

X[ 1 2 3 4 5 6 ]=[ −7 −8 −9 2 4 6 ] X [ 1 2 3 4 5 6 ] 2×3 = [ −7 −8 −9 2 4 6 ] 2×3

So X will be a 2×2 matrix. Consider the matrix X as,

X= [ u w v x ] 2×2

So the final equation becomes,

[ u w v x ][ 1 2 3 4 5 6 ]=[ −7 −8 −9 2 4 6 ] [ u+4w 2u+5w 3u+6w v+4x 2v+5x 3v+6x ]=[ −7 −8 −9 2 4 6 ]

Since, the matrices are equal so their corresponding elements are equal. Compare the elements of the first row.

u+5w=−7(1)

2u+5w=−8(2)

3u+6w=−9(3)

Compare the elements of the second row.

v+4x=2(4)

2v+5x=4(5)

3v+6x=6(6)

Solve equation (1) and (2) to find the value of u and w.

u=1 w=−2

Solve equation (4) and (5) to find the values of v and x.

v=2 x=0

Substitute the above values in the matrix X,

X= [ u w v x ] 2×2 =[ 1 −2 2 0 ]

Thus, the required matrix X is [ 1 −2 2 0 ].