Answer to Question #195741 in Linear Algebra for Mapula Advice

Question

Solve x y z and t in the matrix equation below [3x t+

Answer 1

Given,

$\begin{bmatrix} 3x& y-x \\t+\dfrac{z}{2}& t-z\end{bmatrix} =\begin{bmatrix} 3& 1\\\dfrac{7}{2}& 3\end{bmatrix}$

On comparing we get-

$3x=3\Rightarrow x=1$

Also, $y-x=1\Rightarrow y=1+1\Rightarrow y=2$

Also,

$t+\dfrac{z}{2}=\dfrac{7}{2}~~~~~~~~~~~~~-(1)$

$t-z=3~~~~~~~~-(2)$

Solving eqn.(1) and (2) and we get-

$z=\dfrac{1}{3} , t=\dfrac{10}{3}$

Hence Value of $x=1,y=2,z=\dfrac{1}{3}$ and $t=\dfrac{10}{3}$