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5. Inverse Matrix Method
Solve linear equations 12x+5y=7 and x+y=7 using Using Matrix Method

`=> (12x+5y-7) = 0`

`=> (x+y-7) = 0`

Here `12x+5y=7`, `x+y=7`

Now converting given equations into matrix form
`[[12,5],[1,1]] [[ x ],[ y ]] = [[7],[7]]`

Now, A = `[[12,5],[1,1]]`, X = `[[ x ],[ y ]]` and B = `[[7],[7]]`

`:. AX = B`

`:. X = A^-1 B`

`| A |=|[12,5],[1,1]|`

= 12 × 1 - 5 × 1
= 12 - 5
= 7
`"Here, " | A | = 7 != 0 `

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

`Adj(A)=Adj[[12,5],[1,1]]`

`=[[+(1),-(1)],[-(5),+(12)]]^T`

`=[[1,-1],[-5,12]]^T`

`=[[1,-5],[-1,12]]`

`"Now, "A^(-1)=1/| A | × Adj(A)`

`"Here, "X = A^(-1) × B`

`:. X =1/| A | × Adj(A) × B`

`=1/7 × [[1,-5],[-1,12]] × [[7],[7]]`

` =1/7 ×[[1*7 + -5*7],[-1*7 + 12*7]]`

` =1/7 ×[[-28],[77]]`

` =[[-4],[11]]`



`:.[[ x ],[ y ]] = [[-4],[11]]`

`:. x = -4, y = 11`

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