Question

Find the matrix X such that X [ 1 2 3 4 5 6 ] = [ -7 -8 -9 2 4 6 ]

Answer 1

The matrix given on the R.H.S. of the equation is a 2×3 matrix and the one given on the L.H.S. of the equation is a 2×3 matrix.

Therefore, X has to be a 2×2 matrix.

Now, let X=[

Equating the corresponding elements of the two matrices, we have:

a+4c=−7

b+4d=2

2a+5c=−8

2b+5d=4

3a+6c=−9

3b+6d=6

Now, a+4c=−7⇒a=−7−4c

∴2a+5c=−8⇒−14−8c+5c=−8

⇒−3c=6⇒c=−2

∴a=−7−4(−2)=−7+8=1

Now, b+4d=2⇒b=2−4d

∴2b+5d=4⇒4−8d+5d=4

⇒−3d=0

⇒d=0

∴b=2−4(0)=2

Thus, a=1,b=2,c=−2,d=0

Hence, the required matrix X

Answer 2

Step-by-step explanation:

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