Question

(d) If \[ \begin{bmatrix} 2x - y & x + 2y \\ 2 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 3 \\ 2 & 3 \end{bmatrix}, \] then the values of \( x \) and \( y \) will be:

• A. \( x = 1, y = 1 \)
• B. \( x = \frac{1}{2}, y = \frac{1}{2} \)
• C. \( x = 2, y = 1 \)
• D. \( x = 1, y = \frac{1}{2} \)

Hint:

For matrix equations, equate corresponding elements and solve the resulting system of linear equations.

Answer 1

The Correct Option is D

Equating the elements of the matrices: \[ 2x - y = 1 \quad \text{and} \quad x + 2y = 3. \] Solving these equations simultaneously: From the first equation: \[ y = 2x - 1. \] Substituting \( y \) into the second equation: \[ x + 2(2x - 1) = 3 \quad \Rightarrow \quad x + 4x - 2 = 3 \quad \Rightarrow \quad 5x = 5 \quad \Rightarrow \quad x = 1. \] Substituting \( x = 1 \) into \( y = 2x - 1 \): \[ y = 2(1) - 1 = 1. \] Thus, the values of \( x \) and \( y \) are \( x = 1 \) and \( y = 1 \).