GATE Engineering Mathematics: Linear Algebra – Previous Year Questions
24 GATE previous year questions on Linear Algebra (Engineering Mathematics, Electronics and Communication Engineering) with answers and explanations, from every paper.
- GATE 2017 EC Q11 – Consider the 5 5 matrix A = bmatrix 1 & 2 & 3 & 4 & 5 \\ 5 & 1 & 2 & 3 & 4 \\ 4 & 5 & 1 & 2 & 3 \\ 3 & 4 & 5 & 1 & 2 \\ 2 & 3 & 4 & 5 & 1 bmatrix. It…
- GATE 2017 EC Q12 – The rank of the matrix M = bmatrix 5 & 10 & 10 \\ 1 & 0 & 2 \\ 3 & 6 & 6 bmatrix is
- GATE 2017 EC Q13 – Consider the following statements about the linear dependence of the real valued functions y 1 = 1, y 2 = x and y 3 = x2, over the field of real…
- GATE 2015 EC Q11 – Consider a system of linear equations: x - 2y + 3z = -1, x - 3y + 4z = 1, and -2x + 4y - 6z = k. The value of k for which the system has infinitely…
- GATE 2015 EC Q15 – The value of p such that the vector bmatrix 1 \\ 2 \\ 3 bmatrix is an eigenvector of the matrix bmatrix 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 bmatrix…
- GATE 2016 EC Q11 – Let M4 = I, (where I denotes the identity matrix) and M I, M2 I and M3 I. Then, for any natural number k, M-1 equals:
- GATE 2016 EC Q37 – A sequence x[n] is specified as bmatrix x[n] \\ x[n-1] bmatrix = bmatrix 1 & 1 \\ 1 & 0 bmatrixn bmatrix 1 \\ 0 bmatrix, for n 2. The initial…
- GATE 2018 EC Q21 – Let M be a real 44 matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M…
- GATE 2018 EC Q32 – Consider matrix A=bmatrixk&2k\2-k&k2bmatrix and vector x=bmatrixx 1\ 2bmatrix. The number of distinct real values of k for which the equation Ax= 0…
- GATE 2019 EC Q27 – The number of distinct eigenvalues of the matrix A=bmatrix2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2bmatrix is equal to .
- GATE 2020 EC Q11 – If v 1, v 2,, v 6 are six vectors in R4, which one of the following statements is FALSE?
- GATE 2020 EC Q36 – Consider the following system of linear equations. x 1+2x 2=b 1;2x 1+4x 2=b 2;3x 1+7x 2=b 3;3x 1+9x 2=b 4 Which one of the following conditions…
- GATE 2021 EC Q26 – If the vectors (1.0,-1.0,2.0), (7.0,3.0,x) and (2.0,3.0,1.0) in R3 are linearly dependent, the value of x is .
- GATE 2021 EC Q46 – A real 22 non-singular matrix A with repeated eigenvalue is given as A=bmatrixx&-3.0\\3.0&4.0bmatrix where x is a real positive number. The value of x…
- GATE 2022 EC Q12 – Consider a system of linear equations Ax=b, where A=bmatrix1&-2&3\\-1&2&-3bmatrix, b=bmatrix1\\3bmatrix. This system of equations admits .
- GATE 2022 EC Q37 – Let , be two non-zero real numbers and v 1,v 2 be two non-zero real vectors of size 31. Suppose that v 1 and v 2 satisfy v 1Tv 2=0, v 1Tv 1=1, and v…
- GATE 2023 EC Q11 – Let v 1=bmatrix1\\2\\0bmatrix and v 2=bmatrix2\\1\\3bmatrix be two vectors. The value of the coefficient in the expression v 1= v 2+ e, which…
- GATE 2023 EC Q15 – Let the sets of eigenvalues and eigenvectors of a matrix B be \ k1 k n\ and \ v k1 k n\, respectively. For any invertible matrix P, the sets of…
- GATE 2023 EC Q38 – Let x be an n1 real column vector with length l= xT x. The trace of the matrix P= x xT is
- GATE 2024 EC Q30 – Let R and R3 denote the set of real numbers and the three dimensional vector space over it, respectively. The value of for which the set of vectors…
- GATE 2024 EC Q55 – Consider the matrix bmatrix1&k\\2&1bmatrix, where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
- GATE 2025 EC Q11 – Consider the matrix A below: A=bmatrix2&3&4&5\\0&6&7&8\\0&0&&\\0&0&0&bmatrix For which of the following combinations of , , and , is the rank of A at…
- GATE 2025 EC Q59 – Consider the vectors a=bmatrix1\\1bmatrix, b=bmatrix0\\32bmatrix. For real-valued scalar variable x, the value of x\ ax- b\ 2 is (rounded off to two…
- GATE 2026 EC Q26 – Consider the matrix M=bmatrix2&1&1\\1&3&0\\-1&a&bbmatrix. Which of the following options is/are TRUE if (M)0?