1.

Solve system of linear equations, using matrix method,`5x + 2y = 4``7x + 3 y = 5`

Answer» Given system of equations,
5x+2y=4
7x+3y = 4
`rArr" "[{:(5,2),(7,3):}][{:(x),(y):}]=[{:(4),(5):}]rArrAX=B`
`"Here "A=[{:(5,2),(7,3):}]`
`rArr" "A=[{:(5,2),(7,3):}]=15-14=1ne0`
`therefore` A is invertible.
`"Now "A_(11)=3, A_(12)=-7, A_(21)=-2,A_(22)=5`
`therefore "adj A"=[{:(3,-7),(-2,5):}][{:(3,-2),(-7,5):}]`
`"and "A^(-1)=1/|A|"adj A"=1/1[{:(3,-7),(-2,5):}][{:(3,-2),(-7,5):}]`
From equation (1) ,
`AX=B rArr X=A^(-1)B`
`rArr" "[{:(x),(y):}]=[{:(3,-2),(-7,5):}]=[{:(12-10),(-28+25):}]=[{:(2),(-3):}]`
`therefore" "x=2, y=-3`


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