Question

If $$ A = \begin{pmatrix} 2 & 3 \\ 1 & k \end{pmatrix} $$ and $\det(A) = 7$, find the value of $ k $.

• A. \(1\)
• B. \(2\)
• C. \(5\)
• D. \(4\)

Hint:

Tip: Carefully apply determinant formula and check arithmetic to avoid mistakes.

Answer 1

The Correct Option is C

Step 1: Recall determinant formula 
\[ \det(A) = ad - bc \] For \[ A = \begin{pmatrix} 2 & 3 \\ 1 & k \end{pmatrix}, \] we have \(a=2\), \(b=3\), \(c=1\), and \(d=k\).

Step 2: Write determinant equation 
\[ \det(A) = 2 \times k - 3 \times 1 = 2k - 3 \]

Step 3: Use given determinant value 
\[ 2k - 3 = 7 \implies 2k = 10 \implies k = 5 \]