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Test: Engineering Mathematics- 2 - Computer Science Engineering (CSE) MCQ


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10 Questions MCQ Test GATE Computer Science Engineering(CSE) 2024 Mock Test Series - Test: Engineering Mathematics- 2

Test: Engineering Mathematics- 2 for Computer Science Engineering (CSE) 2024 is part of GATE Computer Science Engineering(CSE) 2024 Mock Test Series preparation. The Test: Engineering Mathematics- 2 questions and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus.The Test: Engineering Mathematics- 2 MCQs are made for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Engineering Mathematics- 2 below.
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Test: Engineering Mathematics- 2 - Question 1

Find the value of x for the singular matrix?

Detailed Solution for Test: Engineering Mathematics- 2 - Question 1

Determinant of a singular matrix is 0

∴ 3×15×(24−3x)=0
∴ 3x=24
∴ x=8

*Answer can only contain numeric values
Test: Engineering Mathematics- 2 - Question 2

If the determinant of the matrix  is 26, then the determinant of the matrix  is


Detailed Solution for Test: Engineering Mathematics- 2 - Question 2

If two rows are interchanged in a determinant then the value of the determinant does not change but sign will change. In the given question, first and third rows are interchanged.

Determinant wil be -26

Test: Engineering Mathematics- 2 - Question 3

The value of the determinant  

Detailed Solution for Test: Engineering Mathematics- 2 - Question 3

Test: Engineering Mathematics- 2 - Question 4

If a matrix A is given by f(x) = a0 + a1x + a2x2+…+ an−1xn−1 + anxn, then the determinant of A is

Detailed Solution for Test: Engineering Mathematics- 2 - Question 4

matrix ‘A’ ⇒ f(x) = a+ a1x + a2x+……….+an−1xn−1 + anxnf(x)

if 2 × 2 matrix then characteristic equation  ⇒ aλ+ bλ + c = 0
⇒ |A| = λ12. = c/a
where ao = c;an = a2 = a 
if 3 × 3 matrix → then characteristic equation ⇒ aλ+ bλ+ cλ + d = 0

∴ For n × n matrix, |A| = λ123….λn

Test: Engineering Mathematics- 2 - Question 5

What is the determinant of the below-given matrix?

Detailed Solution for Test: Engineering Mathematics- 2 - Question 5

Determinant of the given matrix is

 

Δ = (a − b) (a − c) (a − d) (b − c) (b − d)(c − d)

a = 3, b = 5, c = 7, d = 9

∴ Δ = 768

Test: Engineering Mathematics- 2 - Question 6

If  A =  then  the value of adj (adj (A))?

Detailed Solution for Test: Engineering Mathematics- 2 - Question 6


A is upper triangular matrix

∴ product of diagonal elements = |A|
 = 1 × 5 × 8 × 10 = 400

 

Note:

|A||A| is determinant of matrix A

*Answer can only contain numeric values
Test: Engineering Mathematics- 2 - Question 7

What is the rank of A−B where


Detailed Solution for Test: Engineering Mathematics- 2 - Question 7


 

∴ rank is < 3

Also



Hence rank of is A−B is 2

 

Test: Engineering Mathematics- 2 - Question 8

What is the value of A− 9A− 47A?

Detailed Solution for Test: Engineering Mathematics- 2 - Question 8

Characteristic equation of the given matrix is

Every matrix satisfies its own characteristic equation

∴A3 − 9A2 − 47A = 20I

Test: Engineering Mathematics- 2 - Question 9

The factorized form of the following determinant is:

Detailed Solution for Test: Engineering Mathematics- 2 - Question 9


Applying R2 → R2 – R1

Now, expanding from a11.


= (m - l)(n - l)(n + l - m - l)

= (m - l)(n - l)(n - m)

Test: Engineering Mathematics- 2 - Question 10

A 3 × 5 matrix has all its entries equal to 1. The rank of the matrix is

Detailed Solution for Test: Engineering Mathematics- 2 - Question 10

Rank ≤ 3 since all entries are 1,

∴| 3 × 3 submatrices | = | 2 × 2 submatrices | = 0

only 1 × 1 or single entries are ≠ 0

∴ rank = 1

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