Solve Equations 2x+5y=16,3x+y=11 using Inverse Matrix method

Solution:
Here `2x+5y=16`
`3x+y=11`

Now converting given equations into matrix form
`[[2,5],[3,1]] [[x],[y]]=[[16],[11]]`

Now, A = `[[2,5],[3,1]]`, X = `[[x],[y]]` and B = `[[16],[11]]`

`:. AX = B`

`:. X = A^-1 B`

`|A|`

=

`2`   `5`   `3`   `1`

`=2 × 1 - 5 × 3`

`=2 -15`

`=-13`


`"Here, " |A| = -13 != 0`

`:. A^(-1) " is possible."`

`Adj(A)`

=

Adj `2` `5` `3` `1`

=	+   `1`   -   `3`   -   `5`   +   `2`  T

=	`+(1)` `-(3)` `-(5)` `+(2)` T

=	`1` `-3` `-5` `2` T

=	`1` `-5` `-3` `2`

`"Now, "A^(-1)=1/|A| × Adj(A)`

`"Here, "X = A^(-1) × B`

`:. X = 1/|A| × Adj(A) × B`

=

`1/(-13)` ×

`1` `-5` `-3` `2`

×

`16` `11`

=

`1/(-13)` ×

`1×16-5×11` `-3×16+2×11`

=

`1/(-13)` ×

`-39` `-26`

=

`3` `2`

`:.[[x],[y]]=[[3],[2]]`

`:. x=3, y=2`

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