GATE 2026 CE (CE2) – Question 31

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Numerical answer

The eigenvalues of $[A] = \begin{bmatrix} 2 & -3.5 & 6 \\ 3.5 & 5 & 2 \\ 8 & 1 & 8.5 \end{bmatrix}$ are

$\lambda_1 = -1.547$, $\lambda_2 = 12.330$, and $\lambda_3 = 4.711$.

The absolute value of the determinant of matrix $A$ is ______ (*rounded off to two decimal places*).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 89.41 to 90.31

Explanation

The determinant is the product of the eigenvalues: $(-1.547)(12.330)(4.711) = -89.86$, so the absolute value is 89.86. Expanding the determinant directly gives 89.88. The small difference comes from the rounding of the eigenvalues.