GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 13

Question

The determinant of the matrix $A = \begin{pmatrix}
\frac{1}{2}& \alpha & 1 & 1 & 1 & 1 & 1 & 1\\
0 & -2 & 1 & 1 & 2 & -3 & 8 & -9\\
0 & 0 & -88 & 0 & 0 & 0 & 2 & 0\\
0 & 0 & 0 & \frac{1}{22} & 5 & 4 & 3 & 21\\
0 & 0 & 0 & 0 & 0 & 1 & 5 & 0\\
0 & 0 & 0 & 0 & 0 & 110 & 0 & 47\\
0 & 0 & 0 & 0 & 0 & 0 & 48 & 78\\
0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{4}
\end{pmatrix}$ is _________

Answer 1

For an upper triangle matrix, the determinant is simply product of  main (principal) diagonal entries.

Determinant $ = \frac{1}{2} \times -2 \times -88 \times \frac{1}{22} \times 0 \times 110 \times 48 \times \frac{1}{4} = 0.$

So, the correct answer is $0.$