GATE Engineering Mathematics: Linear Algebra – Previous Year Questions

11 GATE previous year questions on Linear Algebra (Engineering Mathematics, Production and Industrial Engineering) with answers and explanations, from every paper.

1. GATE 2021 PI Q34 (1 mark, Numerical answer) – For real x,y and i=-1, (3i+1)x+(4i+4)y+5=0. Find x to one decimal.
2. GATE 2021 PI Q41 (2 marks, Multiple choice) – A=pmatrix8&3\\2&7pmatrix has eigenvalues 5 and 10. For constant α and 2×2 identity I, find eigenvalues of B = A+αI.
3. GATE 2022 PI Q11 (1 mark, Multiple choice) – For vectors a,b,c, find ( a b) c.
4. GATE 2022 PI Q23 (1 mark, Numerical answer) – A=pmatrix3\\2pmatrixpmatrix1&4pmatrix. Find det(A), rounded to nearest integer.
5. GATE 2022 PI Q36 (2 marks, Multiple choice) – When a matrix is squared, which statement is correct?
6. GATE 2023 PI Q11 (1 mark, MTA) – Given A=pmatrix1&-1&4\\3&2&-1\\2&1&-1pmatrix and B=(B ij) 33, B is the skew-symmetric matrix of A. Find B₁₃.
7. GATE 2023 PI Q49 (2 marks, Numerical answer) – For A=pmatrix4&2\\3&3pmatrix, find the eigenvalue associated with eigenvector pmatrix2\\-3pmatrix (integer).
8. GATE 2024 PI Q36 (2 marks, Multiple choice) – A=pmatrixa&b\&-apmatrix. If A² = I, which equation is true?
9. GATE 2025 PI Q11 (1 mark, Multiple choice) – Find the eigenvalues of A=pmatrix0&-1\\1&0pmatrix.
10. GATE 2026 PI Q16 (1 mark, Multiple choice) – Find the possible value(s) of 1/in, where i=-1 and n is an even positive integer.
11. GATE 2026 PI Q38 (2 marks, Multiple choice) – Match the matrices P,Q,R,S to properties 1: singular; 2: triangular; 3: symmetric; 4: trace-free. P=pmatrix-30&17&5\\17&0&-12\\5&-12&4pmatrix,…