Question

If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :

• A. 2 or 10
• B. -2 or 10
• C. 2 or -10
• D. -2 or -10

Hint:

Always equate corresponding elements of matrices when solving matrix equations.

Answer 1

The Correct Option is C

From the given matrix equation, equate the corresponding elements: \[ 2x - 1 = x + 3 \quad \text{and} \quad y^2 - 1 = 35 \] Solving the first equation: \[ 2x - x = 3 + 1 \quad \Rightarrow \quad x = 4 \] Solving the second equation: \[ y^2 = 36 \quad \Rightarrow \quad y = 6 \text{ or } y = -6 \] Thus, \( x - y = 4 - 6 = -2 \) or \( x - y = 4 + 6 = 10 \).
So, the correct answer is 2 or -10.