Question

Given that [ 6 −2 2 3 ] x = ( 10 −4 ), state the order of x. Also find x.

Answer 1

ANSWER

Here, AX=B, where A=[

2

(i) The order of A is 2×2 and order of B is 2×1. Let the order of X be m×n.

Now, AX will exist only if the number of columns of A is equal to the number of rows of X, i.e, m=2

When a matrix of order a×c is multiplied with another matrix of order c×b, the resultant matrix has the order a×b.

Therefore, order of matrix X is 2

Therefore,

2a+b=7...(1)

−3a+4b=6...(2)

From (1), we get b=7−2a. Substitute this value of in (2).

−3a+4(7−2a)=6

⇒−3a+28−8a=6⇒11a=22⇒a=2