## Linear Algebra MCQs

11. 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.

12. 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.

13. 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.

14. 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]"

15. _______________ 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.

16. 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.

17. 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.

18. 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.

19. 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.

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

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