Q : 7     Solve system of linear equations, using matrix method.

            \small 5x+2y=4

            \small 7x+3y=5

Answers (1)
D Divya Prakash Singh

The given system of equations

  \small 5x+2y=4

  \small 7x+3y=5

can be written in the matrix form of AX =B, where

A = \begin{bmatrix} 5 &4 \\ 7& 3 \end{bmatrix}X = \begin{bmatrix} x\\y \end{bmatrix}  and B = \begin{bmatrix} 4\\5 \end{bmatrix}

we have, 

|A| = 15-14=1 \neq 0.

So, A is non-singular, Therefore, its inverse A^{-1} exists.

as we know A^{-1} = \frac{1}{|A|} (adjA)

A^{-1} = \frac{1}{|A|} (adjA) = (adjA) = \begin{bmatrix} 3 &-2 \\ -7& 5 \end{bmatrix}

So, the solutions can be found by X = A^{-1}B = \begin{bmatrix} 3 &-2 \\ -7 & 5 \end{bmatrix}\begin{bmatrix} 4\\5 \end{bmatrix}

\Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 12-10\\ -28+25 \end{bmatrix} = \begin{bmatrix} 2\\-3 \end{bmatrix}

Hence the solutions of the given system of equations;

x = 2 and y =-3.

 

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