GATE · Engineering Mathematics

Matrices and determinants

31 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 31 questions

What is the value of the determinant $5766$ ?
What is the value of the determinant $12 - 4 9$ ?
What is the value of the determinant $- 3 0 08$ ?
What is the value of the determinant $5 - 2 87$ ?
What is the value of the determinant $3927$ ?
What is the value of the determinant $11 0 - 3$ ?
What is the value of the determinant $66 - 2 - 5$ ?
What is the value of the determinant $27 - 5 - 2$ ?
What is the value of the determinant $8 - 3 1 - 2$ ?
What is the value of the determinant $79 - 1 3$ ?
What is the value of the determinant $47 - 5 - 1$ ?
What is the value of the determinant $3 - 3 - 3 - 5$ ?
Find the determinant of the diagonal matrix $500030001$ .
Find the determinant of the diagonal matrix $100020004$ .
Find the determinant of the diagonal matrix $100040001$ .
Find the determinant of the diagonal matrix $300020003$ .
Find the determinant of the diagonal matrix $300010001$ .
Find the determinant of the diagonal matrix $100030005$ .
Find the trace (sum of the diagonal elements) of $A = (5 - 1 44)$ .
Find the trace (sum of the diagonal elements) of $A = (4110)$ .
Find the trace (sum of the diagonal elements) of $A = (- 3 6 66)$ .
Find the trace (sum of the diagonal elements) of $A = (4 - 3 06)$ .
Find the trace (sum of the diagonal elements) of $A = (- 4 4 6 - 1)$ .
Find the trace (sum of the diagonal elements) of $A = (- 2 4 04)$ .
Let $A$ be a $3 \times 3$ matrix with eigenvalues $1$ , $2$ , and $4$ . What is the determinant of the matrix $B = A^{2} - 3 A + 3 I$ ?
For a 3x3 real matrix A, the eigenvalues are 1, -2, and 4. What is the trace of the matrix (A^2 - 3A + 2I)?
Let A be an invertible 3x3 matrix with determinant det(A) = 5. What is the determinant of the matrix 2 * adj(A)?
A system of linear equations is given by: x + y + z = 6, x + 2y + 3z = 10, and x + 2y + λz = μ. For which values of λ and μ does the system possess infinitely many solutions?
If the characteristic equation of a 2x2 matrix A is λ^2 - 5λ + 6 = 0, which expression correctly gives A^(-1) by the Cayley-Hamilton theorem?
What is the rank of the 4x4 matrix whose (i, j)-th entry is given by a_ij = i * j for 1 ≤ i, j ≤ 4?
For the matrix A = [[2, 1], [0, 2]], which of the following is true regarding its geometric and algebraic multiplicities for eigenvalue λ = 2?

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