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

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

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

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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

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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.

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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

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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

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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

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

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

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19. The cofactor is always preceded by a?

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

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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.

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