Test: Linear Algebra


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20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Linear Algebra

Test: Linear Algebra for Electronics and Communication Engineering (ECE) 2022 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Test: Linear Algebra questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Linear Algebra MCQs are made for Electronics and Communication Engineering (ECE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Linear Algebra below.
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Test: Linear Algebra - Question 1

If A is a non–singular matrix and the eigen values of A are 2 , 3 , -3 then the eigen values of A-1 are:

Detailed Solution for Test: Linear Algebra - Question 1
  • If λ1 ,λ2 ,λ3 ....λare the eigen values of a non–singular matrix A, then A-1 has the eigen values  1/λ1 ,1/λ2 ,1/λ3 ....1/λn 
  • Thus eigen values of A-1are 1/2, 1/3, -1/3
Test: Linear Algebra - Question 2

If -1, 2, 3 are the eigen values of a square matrix A then the eigen values of A2 are:

Detailed Solution for Test: Linear Algebra - Question 2
  • If λ1 ,λ2 ,λ3 ....λare the eigen values of  a matrix A, then A2 has the eigen values  λ12 ,λ22 ,λ32 ....λn2 
  • So, eigen values of Aare 1, 4, 9.
Test: Linear Algebra - Question 3

The sum of the eigenvalues of    is equal to: 

Detailed Solution for Test: Linear Algebra - Question 3
  • Since the sum of the eigenvalues of an n–square matrix is equal to the trace of the matrix (i.e. sum of the diagonal elements)
  • So, required sum = 8 + 5 + 5  = 18
Test: Linear Algebra - Question 4

If 2, - 4 are the eigen values of a non–singular matrix A and |A| = 4, then the eigen values of adjA are:

Detailed Solution for Test: Linear Algebra - Question 4

Test: Linear Algebra - Question 5

If 2 and 4 are the eigen values of A then the eigenvalues of AT are

Detailed Solution for Test: Linear Algebra - Question 5

Since, the eigenvalues of A and Aare square so the eigenvalues of AT are 2 and 4.

Test: Linear Algebra - Question 6

If 1 and 3 are the eigenvalues of a square matrix A then A3 is equal to:

Detailed Solution for Test: Linear Algebra - Question 6
  • Since 1 and 3 are the eigenvalues of A so the characteristic equation of A is:
  • Also, by Cayley–Hamilton theorem, every square matrix satisfies its own characteristic equation. So:
Test: Linear Algebra - Question 7

If A is a square matrix of order 3 and |A| = 2 then A (adj A) is equal to:

Detailed Solution for Test: Linear Algebra - Question 7

Test: Linear Algebra - Question 8

If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal to:

Detailed Solution for Test: Linear Algebra - Question 8

Since the product of the eigenvalues is equal to the determinant of the matrix so: |A| = 1 x 2 x 5 = 10

Test: Linear Algebra - Question 9

If the product of matrices

is a null matrix, then θ and Ø differ by:

Detailed Solution for Test: Linear Algebra - Question 9

Test: Linear Algebra - Question 10

If A and B are two matrices such that A +  B and AB are both defined, then A and B are:

Detailed Solution for Test: Linear Algebra - Question 10
  • Since A + B is defined, A and B are matrices of the same type, say m x n. Also, AB is defined.
  • So, the number of columns in A must be equal to the number of rows in B i.e. n = m.
  • Hence, A and B are square matrices of the same order.
Test: Linear Algebra - Question 11

If A is a 3-rowed square matrix such that |A| = 2, then |adj(adj A2)| is equal to:

Detailed Solution for Test: Linear Algebra - Question 11

Test: Linear Algebra - Question 12

 then the value of x is:

Detailed Solution for Test: Linear Algebra - Question 12

Test: Linear Algebra - Question 13

Detailed Solution for Test: Linear Algebra - Question 13

Inverse matrix is defined for square matrix only.

Test: Linear Algebra - Question 14

Detailed Solution for Test: Linear Algebra - Question 14

Test: Linear Algebra - Question 15

A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is:

Detailed Solution for Test: Linear Algebra - Question 15

A must be invertible.

For a set of linear equations, Ax = b. The inverse of matrix A exists (i.e. |A| ≠ 0).

This is the necessary condition for the existence of a solution for this system.

Test: Linear Algebra - Question 16

Select a suitable figure from the four alternatives that would complete the figure matrix.


Detailed Solution for Test: Linear Algebra - Question 16

In each row (as well as each column), the third figure is a combination of all the elements of the first and the second figures.

Test: Linear Algebra - Question 17

For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:

Detailed Solution for Test: Linear Algebra - Question 17

Determinant of a skew-symmetric even ordered matrix A should be a perfect square.

Test: Linear Algebra - Question 18

Detailed Solution for Test: Linear Algebra - Question 18

Test: Linear Algebra - Question 19

Matrix D is an orthogonal matrix    The value of B is:

Detailed Solution for Test: Linear Algebra - Question 19

For orthogonal matrix

Test: Linear Algebra - Question 20

Detailed Solution for Test: Linear Algebra - Question 20

From linear algebra for Anxn triangular matrix . DetA = The product of the diagonal entries of A.

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