Test: Linear Algebra - Civil Engineering (CE) MCQ

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

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## 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.
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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.
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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 the product of matrices

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

Detailed Solution for Test: Linear Algebra - Question 8

Test: Linear Algebra - Question 9

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 9
• 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 10

then the value of x is:

Detailed Solution for Test: Linear Algebra - Question 10

Test: Linear Algebra - Question 11

Detailed Solution for Test: Linear Algebra - Question 11

Inverse matrix is defined for square matrix only.

Test: Linear Algebra - Question 12

Detailed Solution for Test: Linear Algebra - Question 12

Test: Linear Algebra - Question 13

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 13

Test: Linear Algebra - Question 14

One of the eigenvectors of the matrix  is

Detailed Solution for Test: Linear Algebra - Question 14

The characteristic equation ∣A − λD = 0

Corresponding to λ = 4, we have

= 0

= 0 which gives only one independent equation,

-9x + 2y = 0

∴ x/2 = y/9 gives eigen vector (2,9)

Corresponding to λ = −3,

which gives -x + y = 0 (only one independent equation)

∴ x/1 = y/1 which gives (1,1)

So, the eigen vectors are

Test: Linear Algebra - Question 15

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 15

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

Test: Linear Algebra - Question 16

The condition for which the eigenvalues of the matrix

are positive, is

Detailed Solution for Test: Linear Algebra - Question 16

All Eigen values of  are positive

2 > 0

∴ 2 x 2 leading minor must be greater than zero

Test: Linear Algebra - Question 17

Detailed Solution for Test: Linear Algebra - Question 17

Test: Linear Algebra - Question 18

The solution to the system of equations

Detailed Solution for Test: Linear Algebra - Question 18

Test: Linear Algebra - Question 19

If A = then det(A −1 ) is __________ (correct to two decimal places).

Detailed Solution for Test: Linear Algebra - Question 19

Test: Linear Algebra - Question 20

The rank of the matrix  is

Detailed Solution for Test: Linear Algebra - Question 20

No. of non zero rows = 2
rank = 2

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## Engineering Mathematics

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