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Test: Linear Algebra - Software Development MCQ


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15 Questions MCQ Test - Test: Linear Algebra

Test: Linear Algebra for Software Development 2025 is part of Software Development preparation. The Test: Linear Algebra questions and answers have been prepared according to the Software Development exam syllabus.The Test: Linear Algebra MCQs are made for Software Development 2025 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

Which of the following is NOT a property of matrices?

Detailed Solution for Test: Linear Algebra - Question 1

Matrices do not have the property of commutativity, which means that matrix multiplication, in general, is not commutative.

Test: Linear Algebra - Question 2

In linear algebra, the rank of a matrix refers to:

Detailed Solution for Test: Linear Algebra - Question 2

The rank of a matrix refers to the number of linearly independent rows or columns in the matrix.

Test: Linear Algebra - Question 3

Which of the following statements is true about Gauss elimination method?

Detailed Solution for Test: Linear Algebra - Question 3

The Gauss elimination method is commonly used to solve systems of linear equations.

Test: Linear Algebra - Question 4

Which of the following matrices is an identity matrix?

Detailed Solution for Test: Linear Algebra - Question 4

An identity matrix is a square matrix with diagonal elements equal to 1 and all other elements equal to 0.

Test: Linear Algebra - Question 5

What is the determinant of a 3x3 matrix defined as?

Detailed Solution for Test: Linear Algebra - Question 5

The determinant of a 3x3 matrix is calculated by taking the difference between the sum of the products of the elements in the main diagonal and the sum of the products of the elements in the off-diagonal.

Test: Linear Algebra - Question 6

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
C = np.dot(A, B)

print(C)
What will be the output of the above code?

Detailed Solution for Test: Linear Algebra - Question 6

The output of the code is the matrix product of matrices A and B, which is [[7, 10], [15, 22]].

Test: Linear Algebra - Question 7

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
C = np.add(A, B)

print(C)
What will be the output of the above code?

Detailed Solution for Test: Linear Algebra - Question 7

The output of the code is the element-wise sum of matrices A and B, which is [[6, 8], [10, 12]].

Test: Linear Algebra - Question 8

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
C = np.subtract(A, B)

print(C)
What will be the output of the above code?

Detailed Solution for Test: Linear Algebra - Question 8

The output of the code is the element-wise difference of matrices A and B, which is [[-4, -4], [-4, -4]].

Test: Linear Algebra - Question 9

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
C = np.matmul(A, B)

print(C)
What will be the output of the above code?

Detailed Solution for Test: Linear Algebra - Question 9

The output of the code is the matrix product of matrices A and B, which is [[19, 22], [43, 50]].

Test: Linear Algebra - Question 10

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[1], [2]])
C = np.dot(A, B)

print(C)
What will be the output of the above code?

Detailed Solution for Test: Linear Algebra - Question 10

The output of the code is the matrix product of matrices A and B, which is [[3], [7]].

Test: Linear Algebra - Question 11

Consider the following matrix:
A = [[2, 4], [1, 3]]
What is the inverse of matrix A?

Detailed Solution for Test: Linear Algebra - Question 11

The inverse of matrix A is [[1, -1], [-2, 2]].

Test: Linear Algebra - Question 12

Consider the following matrix:
A = [[2, 4], [1, 3]]
What is the determinant of matrix A?

Detailed Solution for Test: Linear Algebra - Question 12

The determinant of matrix A is 6.

Test: Linear Algebra - Question 13

Consider the following matrix:
A = [[2, 4, 6], [1, 3, 5], [0, 1, 2]]
What is the rank of matrix A?

Detailed Solution for Test: Linear Algebra - Question 13

The rank of matrix A is 3.

Test: Linear Algebra - Question 14

Consider the following system of linear equations:
2x + 3y + 4z = 10
5x + 6y + 7z = 20
8x + 9y + 10z = 30
What is the solution for the system of equations?

Detailed Solution for Test: Linear Algebra - Question 14

The solution for the system of linear equations is x = 1, y = 2, z = 3.

Test: Linear Algebra - Question 15

Consider the following matrix:
A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
What is the sum of the diagonal elements of matrix A?

Detailed Solution for Test: Linear Algebra - Question 15

The sum of the diagonal elements of matrix A is 15.

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