Question

What are the values of the given variables in this matrix system?

Answer 1

Given:

The matrix system is given as

`\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}-\begin{bmatrix}{2} & {-5} \\ {10} & {-6}\end{bmatrix}=\begin{bmatrix}{4} & {8} \\ {-1} & {0}\end{bmatrix}`

Required:

We want to find the value of a, b, c and d

Step-by-step explanation:

First we need to simplify the given matrix system

`\begin{gathered} \begin{bmatrix}{a-2} & {b-(-5)} \\ {c-10} & {d-(-6)}\end{bmatrix}=\begin{bmatrix}{4} & {8} \\ {-1} & {0}\end{bmatrix} \\ \\ \begin{bmatrix}{a-2} & {b+5} \\ {c-10} & {d+6}\end{bmatrix}=\begin{bmatrix}{4} & {8} \\ {-1} & {0}\end{bmatrix} \end{gathered}`

by this we can also write

`\begin{gathered} a-2=4 \\ b+5=8 \\ c-10=-1 \\ d+6=0 \end{gathered}`

Now simplify all

`\begin{gathered} a-2=4 \\ a=4+2 \\ a=6 \end{gathered}`
`\begin{gathered} b+5=8 \\ b=8-5 \\ b=3 \end{gathered}`
`\begin{gathered} c-10=-1 \\ c=-1+10 \\ c=9 \end{gathered}`
`\begin{gathered} d+6=0 \\ d=-6 \end{gathered}`

Final answer:

`\begin{gathered} a=6 \\ b=3 \\ c=9 \\ d=-6 \end{gathered}`