solve by matrix method x+y+z=6,x-2y+3z=6, x+y+z=2 Related: NCERT Solutions, Determinants, Exercise 4.6, Class 12, Maths

Question

solve by matrix method x+y+z=6,x-2y+3z=6, x+y+z=2 Related:  NCERT Solutions, Determinants, Exercise 4.6, Class 12, Maths

Answer

Answer

Solving a system of linear equations using matrix method

Given system of linear equations:

x + y + z = 6

x - 2y + 3z = 6

x + y + z = 2

Step 1: Convert the system of equations into matrix form

Write the coefficients of the variables in a matrix and the constants on the right-hand side in another matrix.

$\begin{bmatrix} 1 & 1 & 1 \ 1 & -2 & 3 \ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 6 \ 6 \ 2 \end{bmatrix}$

Step 2: Find the inverse of the coefficient matrix

Find the inverse of the matrix of coefficients using any method like cofactor method, row reduction method, or Gauss-Jordan method.

$\begin{bmatrix} 1 & 1 & 1 \ 1 & -2 & 3 \ 1 & 1 & 1 \end{bmatrix}^{-1} = \begin{bmatrix} -1 & 2 & -1 \ 1 & 1 & -1 \ 0 & -1 & 1 \end{bmatrix}$

Step 3: Multiply the inverse matrix with the constant matrix

Multiply the inverse matrix obtained in the previous step with the constant matrix on the right-hand side of the equation.