1. Solve linear equations x+y=2 and 2x+3y=4 using Inverse matrix Method

Solution:
Here `x+y=2`
`2x+3y=4`

Now converting given equations into matrix form
`[[1,1],[2,3]] [[x],[y]]=[[2],[4]]`

Now, A = `[[1,1],[2,3]]`, X = `[[x],[y]]` and B = `[[2],[4]]`

`:.AX = B`

`:.X = A^-1 B`

`|A|`

=

`1`   `1`   `2`   `3`

`=1 × 3 - 1 × 2`

`=3 -2`

`=1`


`"Here, " |A| = 1 != 0`

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

`Adj(A)`

=

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

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

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

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

`"Now, "A^(-1)=1/|A| × Adj(A)`

`"Here, "X = A^(-1) × B`

`:. X = 1/|A| × Adj(A) × B`

=

`1/(1)` ×

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

×

`2` `4`

=	`3×2-1×4` `-2×2+1×4`

=

`2` `0`

`:.[[x],[y]]=[[2],[0]]`

`:.x=2,y=0`