MTH501 Final Term Solved MCQs

Q2. A matrix that results from applying a single elementary row operation to an identity matrix is called (1 marks)

1. Invertible matrix
2. Singular matrix
3. Scalar matrix
4. Elementary matrix

Correct answer: Invertible matrix

Q3. For an n×n matrix (At)t = (1 marks)

1. At

Q7. A is diagonalizable if (1 marks)

Where

1. D is any matrix and P is an invertible matrix
2. D is a diagonal matrix and P is any matrix
3. D is a diagonal matrix and P is invertible matrix
4. D is a invertible matrix and P is any matrix

(6 )(2 )(9

(6 )(8 )(5 )(4

(6 ) (2 )(9

(6 )(6 )(7 )(4

A PDP 

from book

A square matrix A is said to be diagonalizable if A is similar to a diagonal matrix. i.e. if A = -1 PDP for some invertible matrix P and some diagonal matrix D.

Q8. The inverse of an invertible lower triangular matrix is (1 marks)

1. lower triangular matrix
2. upper triangular matrix
3. diagonal matrix

The standard operations on triangular matrices conveniently preserve the triangular form: the sum and product of two upper triangular matrices is again upper triangular. The inverse of an upper triangular matrix is also upper triangular, and of course we can multiply an upper triangular matrix by a constant and it will still be upper triangular. This means that the upper triangular matrices form a subalgebra of the ring of square matrices for any given size. The analogous result holds for lower triangular matrices. Note, however, that the product of a lower triangular with an upper triangular matrix does not preserve triangularity.