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# CBSE Class 12-science Answered

Example 17 Solve the following system of equations by matrix method. 3x-2y+3z =8 2x+y-z=1 4x-3y+2z = 4
Asked by mahammadsharifdakhani67 | 16 Apr, 2024, 07:43: PM
Expert Answer

Simultaneous linear equations in three variable are

3 x - 2 y + 3 z = 8

2 x + y - z = 1

4x - 3y + 2z = 4

Above equations are written using matrix A as

A Ψ = φ

where Ψ and φ are column vectors

To get the colum vector Ψ = ( x  y  z )T , we need to find inverse of matrix A , i.e. A-1 .

First step to get inverse of matrix A is to get cofactor matrix

Let us denote aij is element of i-th row anf j-th column of matrix A .

Cofactor of aij is value of derminant obtained after leaving t-th row and j-th colum element with sign (-1)i+j

For example cofactor of a11 = 3 is calculated as follows

cofactor of a12 = -8 ;  cofactor of a13 = -10 ;

cofactor of a21 = -5 ;  cofactor of a22 = -6 ; cofactor of a23 = 1 ;

cofactor of a31 = -1 ;  cofactor of a32 = 9 ; cofactor of a33 = 7 ;

Cofactor matrix of matrix A is

Adjoint matrix A+ of matrix A is transpose of cofactor matrix

Inverse matrix A-1 is  Adjoint matrix A+ divided by determinant of matrix A

Determinant of A is calculated as given below

Hence inverse matrix is

Colum vector ψ = ( x y z )T is calculated by multilying colum vector φ = ( 8  1   4 )T by inverse matrix

Hence we get ,  x = 1 ; y =2 ; z = 3

Answered by Thiyagarajan K | 17 Apr, 2024, 11:43: PM

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