Question

The value of $\left| \begin{aligned} & \begin{matrix} 1 & 0 & 0 & 0 \\ 2 & 2 & 0 & 0 \\ 4 & 4 & 3 & 0 \\ 5 & 5 & 5 & 4 \end{matrix}\begin{matrix} 0 \\ 0 \\ 0 \\ 0 \end{matrix} \\ & \begin{matrix} 6 & 6 & 6 & 6 \end{matrix}5 \end{aligned} \right|$ is

• A. 6!
• B. 5!
• C. $1.2^{2}.3.4^{3}.5^{4}.6^{4}$
• D. None

Answer 1

Answer: (B)

5!

Answer 2

The elements in the leading diagonal are 1, 2, 3, 4, 5. On one side of the leading diagonal all the elements are zero.

$\therefore$ The value of the determinant

= The product of the elements in the leading diagonal

= 1.2.3.4.5 = 5!