Question 1
What is the determinant of a 3x3 identity matrix I?
Detailed Solution
The determinant of an identity matrix of any order is always 1.
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GATE CSE Engineering Mathematics – Full Mock Test-1
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Question 2
If A is a 3x3 matrix with $\det(A) = 5, what$ is $\det(2A)$?
Detailed Solution
$\det(kA) = k^n * \det(A)$. For $n=3$, $\det(2A) = 2^3 * 5 = 8 * 5 = 40$.
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Question 3
If matrix A is orthogonal, then $\det(A)$ is always equal to:
Detailed Solution
For an orthogonal matrix A, $A^{T}$ * $A = I$, so $\det(A^{T})\det(A) = (\det(A))^2 = 1 => \det(A) = +/- 1$.
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Question 4
The sum of the eigenvalues of a matrix is equal to its:
Detailed Solution
The sum of all eigenvalues of a square matrix equals the trace (sum of diagonal entries) of the matrix.
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Question 5
The product of the eigenvalues of a matrix is equal to its:
Detailed Solution
The product of all eigenvalues of a square matrix equals its determinant.
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