The GATE Grind

GATE Linear Algebra: Special matrices: projection, orthogonal and idempotent, quadratic forms – Previous Year Questions

5 GATE previous year questions on Special matrices: projection, orthogonal and idempotent, quadratic forms (Linear Algebra, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

  1. GATE 2024 DA Q49 (2 marks, Multiple select) – Let R be the set of real numbers, U be a subspace of R3 and M R3 3 be the matrix corresponding to the projection on to the subspace U. Which of the…
  2. GATE 2025 DA Q38 (2 marks, Multiple choice) – Let \x 1, x 2, , x n\ be a set of linearly independent vectors in Rn. Let the (i, j)-th element of matrix A Rn n be given by A ij = x i x j, 1 i, j n.…
  3. GATE 2025 DA Q50 (2 marks, Multiple select) – Let x 1, x 2, x 3, x 4, x 5 be a system of orthonormal vectors in R10. Consider the matrix A = x 1x 1 + + x 5x 5. Which of the following statements…
  4. GATE 2025 DA Q52 (2 marks, Multiple select) – An n n matrix A with real entries satisfies the property: \ Ax\ 2 = \ x\ 2, for all x Rn, where \ \ denotes the Euclidean norm. Which of the following…
  5. GATE 2026 DA Q52 (2 marks, Multiple select) – Let M = (I n - 1n11T) be a matrix, where 1 = (1, 1, 1, , 1)T Rn and I n is the identity matrix of order n. Which of the following options is/are…