Question

If \( X + Y = \begin{pmatrix} 5 & 3 \\ 0 & 7 \end{pmatrix} \) and \( X - Y = \begin{pmatrix} 7 & 1 2 & 3 \end{pmatrix} \). Then X and Y are

• A. \( X = \begin{pmatrix} 6 & 2 \\ 1 & 5 \end{pmatrix} \text{ and } Y = \begin{pmatrix} -1 & 1 \\ -1 & 2 \end{pmatrix} \)
• B. \( X = \begin{pmatrix} 0 & 5 \\ 1 & 4 \end{pmatrix} \text{ and } Y = \begin{pmatrix} -1 & -1 \\ -1 & 2 \end{pmatrix} \)
• C. \( X = \begin{pmatrix} 6 & 2 \\ 1 & 5 \end{pmatrix} \text{ and } Y = \begin{pmatrix} -1 & -1 \\ -1 & 2 \end{pmatrix} \)
• D. \( X = \begin{pmatrix} 1 & 4 \\ 5 & 0 \end{pmatrix} \text{ and } Y = \begin{pmatrix} 0 & 2 \\ 1 & 1 \end{pmatrix} \)

Hint:

Treat matrix equations like scalar equations for addition/subtraction. Add or subtract equations to isolate one variable, then back-substitute. Always perform element-wise addition/subtraction carefully. Double-check your result against options to catch any simple arithmetic errors.

Answer 1

The Correct Option is A