Question

Given x,y,z terms what is the y value of the solution to the matrix equation below

Answer 1

Given:

`A=\begin{bmatrix}{4} & {5} & {-6} \\ {3} & {-2} & 7 \\ {7} & {-6} & -8\end{bmatrix}^(-1)\begin{cases}{-14} \\ {47} \\ {15}\end{cases}`

Required:

We want to find y-value

Step-by-step explanation:

To find inverse

First we need to find adj of given matric

`adj(A)=\begin{bmatrix}{58} & {7}3 & {-4} \\ {76} & {10} & {59} \\ {23} & {-46} & {-23}\end{bmatrix}`

Now find determinent of matrix A

`\begin{gathered} A=4(16-(-42))-5(-18-49)-6(-18+14) \\ =4*58-5*-73-6(-4) \\ =232+367+24=621 \end{gathered}`

now put the values

`\begin{gathered} (1)/(621)\begin{bmatrix}{58} & {73} & {-4} \\ {76} & {10} & {59} \\ {23} & {-46} & {-23}\end{bmatrix}\begin{cases}{-14} \\ {47} \\ {15}\end{cases} \\ \\ =(1)/(621)\begin{cases}{2559} \\ {291} \\ {2829}\end{cases} \end{gathered}`

Final answer:

A