1. Solve Equations 2x+5y=21,x+2y=8 using Inverse Matrix method

Solution:
Here `2x+5y=21`
`x+2y=8`

Now converting given equations into matrix form
`[[2,5],[1,2]] [[x],[y]]=[[21],[8]]`

Now, A = `[[2,5],[1,2]]`, X = `[[x],[y]]` and B = `[[21],[8]]`

`:. AX = B`

`:. X = A^-1 B`

`|A|`

=

`2`   `5`   `1`   `2`

`=2 × 2 - 5 × 1`

`=4 -5`

`=-1`


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

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

`Adj(A)`

=

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

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

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

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

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

`"Now, "A^(-1)=1/|A| × Adj(A)`

`"Here, "X = A^(-1) × B`

`:. X = 1/|A| × Adj(A) × B`

=

`1/(-1)` ×

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

×

`21` `8`

=

`1/(-1)` ×

`2×21-5×8` `-1×21+2×8`

=

`1/(-1)` ×

`2` `-5`

=

`-2` `5`

`:.[[x],[y]]=[[-2],[5]]`

`:. x=-2, y=5`

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