Question

What is the value of A in the matrix equation below?

Answer 1

A=

`\binom{ - 3 \: \: \: - 14 \: \: \: \: \: \: 7 \: \: \: \: 18}{ - 3 \: \: \: \: \: \: \: \: 2 \: \: \: \: \: \: \:5 \: \: \: \: - 6 }`
Answer:The third image(Option B)

Answer 2

Option (b) is correct.

The matrix A is
`\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}`

Explanation:

Given : A matrix form,

`A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}`

we have to find the value of matrix A

Consider the given matrix form,

`A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}`

when A + B = C

Then A = C - B

That is

`A=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}-\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}`

Subtract the elements in the matching position, we get,

`A=\begin{pmatrix}0-3&\left(-5\right)-9&6-\left(-1\right)&10-\left(-8\right)\\ 3-16&0-\left(-2\right)&\left(-2\right)-3&7-13\end{pmatrix}`

Simplify, we get,

`A=\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}`

Thus, The matrix A is
`\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}`