Answer to Question #190361 in Linear Algebra for Regomoditswe Dibob

Question

Solve for x, y, z, and t in the matrix equation below.  3x y − x t + 1 2 z t − z  =  3 1 7 2 3  .

Answer 1

To solve for x, y , z, t

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

On comparing:

$\Rightarrow 3x=3\\\Rightarrow\boxed{x=1}$

$\Rightarrow y-x=1\\\Rightarrow y-1=1\\\Rightarrow \boxed{y=2}$

and

$t+\frac{1}{2}z=\frac{7}{2}\ \ ......(i)\\\ \\t-z=3\ \ .........(ii)\\Subtracting\ equations \ (ii)\ from\ (i)\\We\ get\\\boxed{z=\frac{1}{3}}\\and\ \\t-z=3\\t-\frac{1}{3}=3\\\boxed{t=\dfrac{10}{3}}$