GATE 2026 Engineering Mathematics PYQs | Linear Algebra

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Question 1

Consider 4 × 4 matrices with their elements from {𝟎, 𝟏}. What is the number of such matrices with even number of 𝟏s in every row and every column? [ MCQ || GATE 2026 Set-1 || 1 Marks]

  • 512

  • 1025

  • 1023

  • 255

Question 2

For 𝑛 > 1, the maximum multiplicity of any eigenvalue of an 𝑛 × 𝑛 matrix with elements from ℝ is [ MCQ || GATE 2026 Set-1 || 1 Marks]

  • n

  • n-1

  • 1

  • n+1

Question 3

Let 𝑛 > 1. Consider an 𝑛 × 𝑛 matrix 𝑀 with its elements from ℝ. Let the vector (0, 1, 0, 0, … , 0) ∈ ℝ𝑛 be in the null space of 𝑀. Which of the following options is/are always correct? [ MSQ || GATE 2026 Set-1 || 1 Marks]

  • Determinant of 𝑀 is 1

  • Determinant of 𝑀 is 0

  • Rank of 𝑀 is 1

  • There are at least two non-zero vectors in the null space of M

Question 4

Consider the system of linear equations given below.

𝑎𝑥 + 𝑦 = 𝑏
16𝑥 + 𝑎𝑦 = 24

Suppose the values of 𝑎 and 𝑏 are chosen such that the system of linear equations produce multiple solutions. Then the product of 𝑎 and 𝑏 is [ NAT || GATE 2026 Set-2 || 1 Marks]

There are 4 questions to complete.

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