# Linear Algebra MCQ Questions And Answers

This section focuses on "Linear Algebra" in Data Science. These Linear Algebra Multiple Choice Questions (MCQ) should be practiced to improve the Data Science skills required for various interviews (campus interview, walk-in interview, company interview), placements, entrance exams and other competitive examinations.

1. Suppose that price of 2 ball and 1 bat is 100 units, then What will be representation of problems in Linear Algebra in the form of x and y?

A. 2x + y = 100

B. 2x + 2y = 100

C. 2x + y = 200

D. x + y = 100

View Answer

Ans : A

Explanation: Suppose the price of a bat is Rs 'x' and the price of a ball is Rs 'y'. Values of 'x' and 'y' can be anything depending on the situation i.e. 'x' and 'y' are variables.
2x + y = 100 is the answer.

2. What is the first step in linear algebra?

A. Let's complicate the problem

B. Solve the problem

C. Visualise the problem

D. None Of the above

View Answer

Ans : C

Explanation: Visualise the problem is the first step in linear algebra.

3. A linear equation in three variables represents a?

A. flat objects

B. line

C. Planes

D. Both A and C

View Answer

Ans : C

Explanation: A linear equation in 3 variables represents the set of all points whose coordinates satisfy the equations.Basically, a linear equation in three variables represents a plane.

4. How many ways a set of three planes can intersect?

A. 3

B. 4

C. 5

D. 6

View Answer

Ans : B

Explanation: There are 4 possible cases : No intersection at all, Planes intersect in a line, They can intersect in a plane, All the three planes intersect at a point.

5. Which of the following is not a type of matrix?

A. Square Matrix

B. Scalar Matrix

C. Trace Matrix

D. Term Matrix

View Answer

Ans : D

Explanation: Term Matrix is not a type of matrix in linear algebra.

6. The matrix which is the sum of all the diagonal elements of a square matrix?

A. Diagonal matrix

B. Trace matrix

C. Identity matrix

D. Both A and B

View Answer

Ans : B

Explanation: Trace : It is the sum of all the diagonal elements of a square matrix.

7. Multiplication of a matrix with a scalar constant is called?

A. Complex multiplication

B. Linear multiplication

C. Scalar multiplication

D. Constant multiplication

View Answer

Ans : C

Explanation: Multiplication of a matrix with a scalar constant is called scalar multiplication.

8. Which of the following is false?

A. we have a constant scalar 'c' and a matrix 'A'. Then multiplying 'c' with 'A' gives : c[Cij] = [c*Aij]

B. The multiplication of two matrices of orders i*j and j*k results into a matrix of order i*k.

C. Two matrices will be compatible for multiplication only if the number of columns of the first matrix and the number of rows of the second one are same.

D. Transposition simply means interchanging the row and column index.

View Answer

Ans : A

Explanation: we have a constant scalar 'c' and a matrix 'A'. Then multiplying 'c' with 'A' gives : "c[Aij] = [c*Aij]"

9. Which of the following is correct method to solve matrix equations?

A. Row Echelon Form

B. Inverse of a Matrix

C. Both A and B

D. None Of the above

View Answer

Ans : C

Explanation: The two methods to solve matrix equations : Row Echelon Form, Inverse of a Matrix

10. _______________ is equal to the maximum number of linearly independent row vectors in a matrix.

A. Row matrix

B. Rank of a matrix

C. Term matrix

D. Linear matrix

View Answer

Ans : B

Explanation: Rank of a matrix is equal to the maximum number of linearly independent row vectors in a matrix.

11. What is true regarding Determinant of a Matrix?

A. The concept of determinant is applicable to square matrices only.

B. To find determinant, subtract diagonal elements together.

C. determinant is a vector value that can be computed from the elements of a Trace matrix

D. Both A and C

View Answer

Ans : A

Explanation: The concept of determinant is applicable to square matrices only is true regarding Determinant of a Matrix.

12. Vectors whose direction remains unchanged even after applying linear transformation with the matrix are called?

A. Eigenvalues

B. Eigenvectors

C. Cofactor matrix

D. Minor of a matrix

View Answer

Ans : B

Explanation: vectors whose direction remains unchanged even after applying linear transformation with the matrix are called Eigenvectors for that particular matrix.

13. The concept of Eigen values and vectors is applicable to?

A. Scalar matrix

B. Identity matrix

C. Upper triangular matrix

D. Square matrix

View Answer

Ans : D

Explanation: The concept of Eigen values and vectors is applicable to square matrices only.

14. What will be output for the following code?

A<-matrix(c(30,31,40,41,50,51,60,61,70),nrow = 3,byrow = T)
e <- eigen(A)
e$values
e$vectors

A. 148.737576 5.317459 -4.055035

B. 147.737576 5.317459 -3.055035

C. 147.737576 6.317459 -3.055035

D. 146.737576 4.317459 -4.055035

View Answer

Ans : B

Explanation: 147.737576 5.317459 -3.055035 is the output for the following code.

15. Singular matrix are?

A. non-invertible

B. invertible

C. Both non-invertible and invertible

D. None Of the above

View Answer

Ans : A

Explanation: Singular matrix are non-invertible

16. Singular Value Decomposition is some sort of generalisation of __________ decomposition.

A. Singular

B. Eigen vector

C. Eigen value

D. None Of the above

View Answer

Ans : C

Explanation: Singular Value Decomposition is some sort of generalisation of Eigen value decomposition.

17. What Will be output of det(A)?

B<-matrix(c(30,31,40,41,50,51,60,61,70),nrow = 3,byrow = T)
A<-solve(B)
det(A)

A. 0.0004166667

B. -0.0004166668

C. 0.0004166668

D. -0.0004166667

View Answer

Ans : D

Explanation: Option D will be output for the following code

18. The cofactor is always preceded by a?

A. positive (+) sign

B. negative (-) sign

C. positive (+) or negative (-) sign

D. With decimal

View Answer

Ans : C

Explanation: The cofactor is always preceded by a positive (+) or negative (-) sign, depending whether the element is in a + or - position.

19. Which of the following is correct application for Eigenvectors?

A. computer vision

B. physics

C. machine learning

D. All of the above

View Answer

Ans : D

Explanation: Eigenvectors find a lot of applications in different domains like computer vision, physics and machine learning.

20. Which of the following is false?

A. Order of matrix : If a matrix has 3 rows and 4 columns, order of the matrix is 3*4 i.e. row*column.

B. Row matrix : A matrix consisting only of columns.

C. Column matrix : The matrix which consists of only 1 column.

D. Row matrix : A matrix consisting only of row.

View Answer

Ans : B

Explanation: Row matrix : A matrix consisting only of columns is false

Discussion