Question

What is the value of the element in row 1, column 1 of matrix C?

Answer 1

-3y

------

4

Explanation:

I just took that and got it right

Answer 2

Option A is correct.

Explanation:

We given with
`\begin{bmatrix}4&y\\0&1\end{bmatrix}X=\begin{bmatrix}y\\4\end{bmatrix}`

We have to find Element in row 1 and column 1 of Matrix C.

Matrix C is Matrix X.

So, we have

`X=\begin{bmatrix}4&y\\0&1\end{bmatrix}^(-1)\begin{bmatrix}y\\4\end{bmatrix}`

So first we find inverse of first matrix,

Inverse of matrix A is given by
`(1)/(\left|A\right|)Adj\,A`

let,
`A=\begin{bmatrix}4&y\\0&1\end{bmatrix}`

then,

`Adj\,A=\begin{bmatrix}1&-y\\0&4\end{bmatrix}`

|A| = 4 × 1 - 0 × y = 4

So,
`X=(1)/(\left|A\right|)Adj\,A*\begin{bmatrix}y\\4\end{bmatrix}`

`=(1)/(4)\begin{bmatrix}1&-y\\0&4\end{bmatrix}\begin{bmatrix}y\\4\end{bmatrix}`

`=(1)/(4)\begin{bmatrix}1* y+(-y)*4\\0* y+4*4\end{bmatrix}`

`=(1)/(4)\begin{bmatrix}y-4y\\16\end{bmatrix}`

`=(1)/(4)\begin{bmatrix}-3y\\16\end{bmatrix}`

`=\begin{bmatrix}(-3y)/(4)\\(16)/(4)\end{bmatrix}`

`=\begin{bmatrix}(-3y)/(4)\\4\end{bmatrix}`

Element at row 1 and column 1 of matrix is
`(-3y)/(4)`

Therefore, Option A is correct.