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# 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

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

3. A linear equation in three variables represents a?

A. flat objects
B. line
C. Planes
D. Both A and C

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

A. 3
B. 4
C. 5
D. 6

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

A. Square Matrix
B. Scalar Matrix
C. Trace Matrix
D. Term Matrix

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

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

A. Complex multiplication
B. Linear multiplication
C. Scalar multiplication
D. Constant 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.

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

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

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

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

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

A. Scalar matrix
B. Identity matrix
C. Upper triangular matrix
D. Square matrix

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

15. Singular matrix are?

A. non-invertible
B. invertible
C. Both non-invertible and invertible
D. None Of the above

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

A. Singular
B. Eigen vector
C. Eigen value
D. None Of the above

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

18. The cofactor is always preceded by a?

A. positive (+) sign
B. negative (-) sign
C. positive (+) or negative (-) sign
D. With decimal

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

A. computer vision
B. physics
C. machine learning
D. All of the above

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.