Question

If \( A \) and \( B \) are two matrices such that \[ 3A + B = \begin{pmatrix} 9 & 11 & 3 \\ 12 & 14 & 19 \end{pmatrix} \] and \[ 2A - 3B = \begin{pmatrix} -16 & 11 & 2 \\ -3 & -22 & 9 \end{pmatrix}, \] then the matrix \( B \) is

• A. \( \begin{pmatrix} 6 & -1 & 0 \\ 3 & 8 & 1 \end{pmatrix} \)
• B. \( \begin{pmatrix} 3 & -1 & 0 \\ 2 & 1 & 1 \end{pmatrix} \)
• C. \( \begin{pmatrix} 8 & 0 & -1 \\ 3 & 1 & 2 \end{pmatrix} \)
• D. \( \begin{pmatrix} 5 & 3 & -1 \\ 0 & 1 & 2 \end{pmatrix} \)
• E. \( \begin{pmatrix} 1 & -3 & 4 \\ 3 & 0 & 2 \end{pmatrix} \)

Hint:

In matrix equations, elimination works exactly like simultaneous equations. Always verify with options if arithmetic gets heavy.

Answer 1

The Correct Option is B