To find the value of the element in row 1, column 1 of the given matrix [tex]\( X \)[/tex], we need to analyze the matrix equation:
[tex]\[ \begin{bmatrix} 4 & y \\ 0 & 1 \end{bmatrix} x = \begin{bmatrix} y \\ 4 \end{bmatrix} \][/tex]
Given the options:
- [tex]\(-\frac{3y}{4}\)[/tex]
- 4
- 8
- 0
we are particularly interested in the element at row 1, column 1 of the matrix [tex]\( X \)[/tex].
The matrix provided:
[tex]\[ A = \begin{bmatrix} 4 & y \\ 0 & 1 \end{bmatrix} \][/tex]
and the vector:
[tex]\[ x = \begin{bmatrix} y \\ 4 \end{bmatrix} \][/tex]
In this context, the element in row 1, column 1 of the matrix [tex]\( A \)[/tex] is clearly:
[tex]\[ A[0, 0] = 4 \][/tex]
Therefore, the value of the element in row 1, column 1 of the matrix [tex]\( A \)[/tex] is:
[tex]\[ \boxed{4} \][/tex]
