Algebra

. Solve system of linear equations, using matrix method. x - y + 2z = 7 3x + 4y - 5z = -5 2x - y + 3z = 12

samrat

12 Years agoGrade

1 Answer

SHAIK AASIF AHAMED

11 Years ago

Hello student,
Please find the answer to your question below
writing given equations in the form of matrix we get
AX=B
$\begin{bmatrix} 1 & -1& 2\\ 3& 4&-5 \\ 2&-1 &3 \end{bmatrix}\begin{bmatrix} x\\ y\\ z \end{bmatrix}=\begin{bmatrix} 7\\-5 \\ 12\end{bmatrix}$
$\begin{bmatrix} x\\ y\\ z \end{bmatrix}=1/4\begin{bmatrix} 7 & 1&-3 \\ -19& -1 & 11\\ -11& -1 &7 \end{bmatrix}\begin{bmatrix} 7\\-5 \\ 12\end{bmatrix}$
on solving we get x=2,y=1 and z=3
Hence the system of equations is consistent and has a unique solution