Find the value of `a` if `[a-b2a+c2a-b3c+d]=[-1 5 0 13]`

Answer

`a=1, b=2, c=3, d=4`

Explanation

`[(a-b,2a+c),(2a-b,3c+d)]=[(-1,5),(0,13)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get
`a-b=-1` (1)
`2a-b=0` (2)
`2a+c=5` (3)
`3c+d=13` (4)
From (2), we have
`b=2a`
Then, from (1), we have
`a-2a=-1`
or `a=1`
`implies b=2`
Now, from (3), we have
`2xx1+c=5`
or `c=3`
From (4), we have
`3xx3+d=13`
or `9+d=13` or `d=4`
`:. a=1, b=2, c=3` and `d=4`