Question

If \( \begin{pmatrix} 1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a \end{pmatrix} \) is singular, then the value of \( a \) is:

• A. \( a = -6 \)
• B. \( a = 5 \)
• C. \( a = -5 \)
• D. \( a = 6 \)
• E. \( a = 0 \)

Hint:

If the rows of a matrix are in an Arithmetic Progression (A.P.), the determinant is often zero. Notice here rows 1 and 2 differ by \( (0, 1, 1) \). For row 3 to continue this, \( a \) must be 6.

Answer 1

The Correct Option is D