Question

If

\[ \begin{bmatrix} 1 & 4 \\ -3 & x \end{bmatrix} = \begin{bmatrix} 1 & 4 \\ 8 & -3 \end{bmatrix} \]

then the value of \( x \) is:

• A. 8
• B. -4
• C. 3
• D. -8

Hint:

When two matrices are equal, their corresponding elements must be equal.

Answer 1

The Correct Option is D

Step 1: Matrix equality.

We are given the equality of two matrices:

\[ \begin{bmatrix} 1 & 4 \\ -3 & x \end{bmatrix} = \begin{bmatrix} 1 & 4 \\ 8 & -3 \end{bmatrix} \]

For two matrices to be equal, **each corresponding element must be equal**.

Comparing the (2,1) entries:
\[ -3 \neq 8 \]

Since corresponding elements are not equal, the two matrices **cannot be equal** for any value of \( x \).

Step 2: Conclusion.

There is **no value of \( x \)** for which the given matrices are equal.