Test: Linear Algebra - Civil Engineering (CE) MCQ

# Test: Linear Algebra - Civil Engineering (CE) MCQ

Test Description

## 20 Questions MCQ Test Engineering Mathematics - Test: Linear Algebra

Test: Linear Algebra for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: Linear Algebra questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Linear Algebra MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Linear Algebra below.
Solutions of Test: Linear Algebra questions in English are available as part of our Engineering Mathematics for Civil Engineering (CE) & Test: Linear Algebra solutions in Hindi for Engineering Mathematics course. Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Attempt Test: Linear Algebra | 20 questions in 60 minutes | Mock test for Civil Engineering (CE) preparation | Free important questions MCQ to study Engineering Mathematics for Civil Engineering (CE) Exam | Download free PDF with solutions
 1 Crore+ students have signed up on EduRev. Have you?
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

The eigenvalues of a matrix A are the roots of the characteristic equation of A, which are invariant under the transpose operation. This means that the matrix A and its transpose AT have the same eigenvalues.

Given that 2 and 4 are the eigenvalues of A, the eigenvalues of AT will also be 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

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

Consider a 3 × 3 matrix A whose (i, j)-th element, ai,j = (i − j)3. Then the matrix A will be

Detailed Solution for Test: Linear Algebra - Question 16

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.

## Engineering Mathematics

61 videos|113 docs|94 tests
Information about Test: Linear Algebra Page
In this test you can find the Exam questions for Test: Linear Algebra solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Linear Algebra, EduRev gives you an ample number of Online tests for practice

## Engineering Mathematics

61 videos|113 docs|94 tests