Question

If $A=\left[\begin{array}{ccc}5& 8& 1\\ 0& 2& 1\\ 4& 3& -1\end{array}\right],B=\left[\begin{array}{c}2\\ -1\\ 3\end{array}\right]$ and $AX=B$ then find $X$

Answer 1

$A=\left[\begin{array}{ccc}5& 8& 1\\ 0& 2& 1\\ 4& 3& -1\end{array}\right]B=\left[\begin{array}{c}2\\ -1\\ 3\end{array}\right]$

$AX=B$

$\left[\begin{array}{ccc}5& 8& 1\\ 0& 2& 1\\ 4& 3& -1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}2\\ -1\\ 3\end{array}\right]$

$5x+8y+z=2$.................(i)

$2y+z=-1\Rightarrow z=-(1+2y)$

$4x+3y-z=3$...................(ii)

$5x+8y-1-2y=2$...............replacing value of $z$ in eq. (i)

$4x+3y+1+2y=3$...............replacing value of $z$ in eq. (ii)

$5x+6y=3$ .... (iii)

$4x+5y=2$ ....(iv)

Now, (iii)$\times$5-(iv)$\times$6

we get, $x=3$

Replacing value of $x$ in eq. i

we get,$y=-2$

$z=-(1+2(-2\left)\right)$

$z=3$

$x=3;y=-2$ and $z=3$

$\left[\begin{array}{c}3\\ -2\\ 3\end{array}\right]=x$.