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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.
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
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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