Question

If A =$\begin{bmatrix}2 & 4 \\\4 & 3 \end{bmatrix}$, X =$\begin{bmatrix}n \\\1 \end{bmatrix}$,B =$\begin{bmatrix}8 \\\11 \end{bmatrix}$,and AX = B, then the value of n will be:

• A. 0
• B. 1
• C. 2
• D. not defined

Answer 1

Answer: (C)

2

Answer 2

Solution: We are solving the equation AX = B, where:

$A = \begin{bmatrix} 2 & 4 \\\ 4 & 3 \end{bmatrix}, \quad X = \begin{bmatrix} n \\\ 1 \end{bmatrix}, \quad B = \begin{bmatrix} 8 \\\ 11 \end{bmatrix}.$

Substitute X into AX:

$\begin{bmatrix} 2 & 4 \\\ 4 & 3 \end{bmatrix} \begin{bmatrix} n \\\ 1 \end{bmatrix} = \begin{bmatrix} 2n + 4 \\\ 4n + 3 \end{bmatrix}.$

Equate with B:

$\begin{bmatrix} 2n + 4 \\\ 4n + 3 \end{bmatrix} = \begin{bmatrix} 8 \\\ 11 \end{bmatrix}.$

From the first equation:

$2n + 4 = 8 \quad \Rightarrow \quad 2n = 4 \quad \Rightarrow \quad n = 2.$

Verify with the second equation:

$4n + 3 = 11 \quad \Rightarrow \quad 4(2) + 3 = 11,$ which is true.

Thus, $n = 2.$