Answer to Question #195741 in Linear Algebra for Mapula Advice

Question #195741

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


1
Expert's answer
2021-05-20T17:17:36-0400

Given,

[3xyxt+z2tz]=[31723]\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=3x=13x=3\Rightarrow x=1


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


Also,


t+z2=72             (1)t+\dfrac{z}{2}=\dfrac{7}{2}~~~~~~~~~~~~~-(1)


tz=3        (2)t-z=3~~~~~~~~-(2)


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


z=13,t=103z=\dfrac{1}{3} , t=\dfrac{10}{3}


Hence Value of x=1,y=2,z=13x=1,y=2,z=\dfrac{1}{3} and t=103t=\dfrac{10}{3}



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