Question

Let \(A = \begin{bmatrix} a & -1 & -a 0 & 1 & -1 1 & 0 & 4 \end{bmatrix}\). If \(|A| = 26\), then the value of \(a\) is equal to

• A. 5
• B. 4
• C. 6
• D. 7
• E. 2

Hint:

For a 3×3 matrix, expand along the first row: \(\sum (-1)^{1+j} a_{1j} M_{1j}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Find the determinant of the 3×3 matrix and set it equal to 26.

Step 2: Detailed Explanation:
\(|A| = a(1 \cdot 4 - (-1) \cdot 0) - (-1)(0 \cdot 4 - (-1) \cdot 1) + (-a)(0 \cdot 0 - 1 \cdot 1)\)
\(= a(4 - 0) + 1(0 + 1) - a(0 - 1)\)
\(= 4a + 1 - a(-1) = 4a + 1 + a = 5a + 1\)
Given \(5a + 1 = 26 \Rightarrow 5a = 25 \Rightarrow a = 5\)

Step 3: Final Answer:
\(a = 5\).