If [[2,-1],[1,0],[-3,4]]A=[[-1,-8,-10],[...

If `[[2,-1],[1,0],[-3,4]]A=[[-1,-8,-10],[1,-2,-5],[9,22,15]]` , then sum of all the elements of matrix `A` is

A

0

B

1

C

2

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:

B

Since the product matrix is `3xx3` matrix and the pre-multiplier of a is a `3xx2` matrix, therefore A is `2xx3` matrix. Let
`A=[(l,m,n),(x,y,z)]`. Then the given equation becomes
`[(2,-1),(1,0),(-3,4)][(l,m,n),(x,y,z)]=[(-1,-8,-10),(1,-2,-5),(9,22,15)]`
or `[(2l-x,2m-y,2n-z),(l,m,x),(-3l+4x,-3m+4y,-3n+4z)]=[(-1,-8,-10),(1,-2,-5),(9,22,15)]`
or `2l-x=-1, 2m-y=-8, 2n -z=-10`,
`l=1, m=-2, n=-5`
`implies x=3, y=4, z=0, l=1, m=-2, n=-5`
`implies A=[(l,m,n),(x,y,z)]=[(1,-2,-5),(3,4,0)]`

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