Test: Matrices - Civil Engineering (CE) MCQ

# Test: Matrices - Civil Engineering (CE) MCQ

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## 15 Questions MCQ Test Engineering Mathematics - Test: Matrices

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

### Comprehension: Direction: Based on the following information, answer the questions: Abhi, Badri, and Chintan were given the task of creating a square matrix of order 3. Below are the matrices created by them. A, B, and C are the matrices created by Abhi, Badri, and Chintan respectively. Let matrix B = P + Q, where P is a symmetric matrix and Q is a skew - symmetric matrix. What is Q?

Detailed Solution for Test: Matrices - Question 1

For any matrix A, (A + A’) is always symmetric and (A - A') is always skew-symmetric.

where P = 1/2(A+ A'), a symmetric matrix and Q = 1/212(A - A'), is a skew-symmetric matrix.

Caluclation:

∴ Required symmetric matrix Q
= 1/2 (B-B')

which is the required answer.

Test: Matrices - Question 2

### Direction: Based on the following information, answer the questions: Abhi, Badri, and Chintan were given the task of creating a square matrix of order 3. Below are the matrices created by them. A, B, and C are the matrices created by Abhi, Badri, and Chintan respectively. What is (AT)T

Detailed Solution for Test: Matrices - Question 2

If A is any matrix, the (AT)T = A.

We have,

∴ (AT)T

= A

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Test: Matrices - Question 3

### If  is a symmetric matrix then x

Detailed Solution for Test: Matrices - Question 3

Given:
A is a symmetric matrix,
⇒ AT = A or aij = aji

So, by property of symmetric matrices

Test: Matrices - Question 4

lf the order of A is 4 × 3, the order of B is 4 × 5 and the order of C is 7 × 3, then the order of (ATB)T CT is

Detailed Solution for Test: Matrices - Question 4

Given:
Order of A is 4 × 3, the order of B is 4 × 5 and the order of C is 7 x 3
The transpose of the matrix obtained by interchanging the rows and columns of the original matrix.
So, order of AT is 3 × 4 and order of CT is 3 × 7
Now,
ATB = {3 x 4} {4 × 5} = 3 x 5
⇒ Order of ATB is 3 x 5
Hence order of (ATB)T is 5 x 3
Now order of (ATB)T CT = {5 x 3} {3 x 7} = 5 x 7
∴ Order of (ATB)T CT is 5 x 7

Test: Matrices - Question 5

If then the value of x is

Detailed Solution for Test: Matrices - Question 5

⇒ [(2x - 9)x + 8 x 4x] = 0

⇒ [2x2 - 9x + 32x] = 0

⇒ 2x2 + 23x = 0

⇒ x(2x + 23) = 0

⇒ x = 0 or - 23/2

Test: Matrices - Question 6

Given that the determinant of the matrix

is -12, the determinant of the matrix

Detailed Solution for Test: Matrices - Question 6

Let D = -12 for the given matrix

(Taking 2 common from each row)

∴Det(A) =​ (2)3 × D

8x − 12 = −96​

Test: Matrices - Question 7

If A is an Involuntary matrix and I is a unit matrix of same order, then (I − A) (I + A) is

Detailed Solution for Test: Matrices - Question 7

Given that A is involuntary matrix,
⇒ A2 = I
Now,
(I − A) (I + A) = I2 – IA + AI − A2
⇒ I – A + A – I         (∵ A2 = I)
⇒ 0
∴ (I − A) (I + A) is zero matrix.

Test: Matrices - Question 8

The matrix   has one Eigenvalue equal to 3. The sum of the other two Eigenvalues is

Detailed Solution for Test: Matrices - Question 8

Sum of the eigen values of matrix is
= sum of diagonal values present in the matrix

Test: Matrices - Question 9

Consider the following question and decide which of the statements is sufficient to answer the question.
Find the value of n, if
Statements∶
1. AB = A
2.

Detailed Solution for Test: Matrices - Question 9

From statement 1∶
AB = A
We cannot find anything from this statement.
From statement 2∶

We cannot find anything from this statement.
Combining statement 1 and 2∶

∴ We cannot find the value of n from both statements together.

Test: Matrices - Question 10

If A2 - 2A - I = 0,then inverse of A is

Detailed Solution for Test: Matrices - Question 10

Given: A2 - 2A - I = 0
⇒ A.A - 2A = I
Post multiply by A-1, we get
⇒ AAA-1 - 2AA-1 = IA-1
⇒ AI - 2I = A-1             [∵ AA -1 = A - 1A = I]
∴ A-1 = A - 2
the inverse of A is A - 2

Test: Matrices - Question 11

If  then the value of A4 is

Detailed Solution for Test: Matrices - Question 11

Now,

Hence Option 1st is correct answer.

Test: Matrices - Question 12

find (AB)T

Detailed Solution for Test: Matrices - Question 12

Given

Test: Matrices - Question 13

The transformation matrix for mirroring a point in x-y plane about the line y=x is given by

Detailed Solution for Test: Matrices - Question 13

The transformation matrix for mirroring a point in x-y plane about the line y = x is

Test: Matrices - Question 14

In matrix equation [A]{X} = {R},

One of the eigenvalues of matrix [A] is

Detailed Solution for Test: Matrices - Question 14

Test: Matrices - Question 15

Consider the matrix

The number of distinct eigenvalues of P is

Detailed Solution for Test: Matrices - Question 15

Given: A =

It is an upper triangular matrix. It's diagonal elements are eigen values.
The eigen values of the matrix are 1, 1, 1.
∴ Number of distinct eigen values = 1
Hence, option (B) is correct.

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## Engineering Mathematics

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