Find the values of a, b, c, and d from the following equation:`[[2a+b, a-2b],[5c-d,4c+3d]]=[[4,-3], [11,24]]`

Explanation

Given two matrices are equal,
`[[2a+b, a-2b],[5c-d,4c+3d]]=[[4,-3], [11,24]]`
We know that if two matrices are equal then the elements of each matrices are also equal.
`therefore` 2a+b=4 ...(1) and
a-2b=-3 ...(2) and
5c-d=11 ...(3) and
4c+3d=24 ...(4)
Multiplying equation (1) by 2 and adding to equation (2),
4a+2b+a-2b=8-3
`implies` 5a=5
`implies` a=1
Now, Putting the value of a in equation (1),
`2xx1`+b=4
`implies`2+b=4
`implies` b=4-2
`implies` b=2
Multiplying equation (3) by 3 and adding to equation (4),
15c-3d+4c+3d=33+24
`implies` 19c=57
`implies` c=3
Now, Putting the value of c in equation (4), `4xx3`+3d=24
`implies` 12+3d=24
`implies` 3d=24-12
`implies` 3d=12
`implies` d=4
`therefore` a=1, b=2, c=3 and d=4.