Explore topic-wise MCQs in Linear Algebra.

This section includes 6 Mcqs, each offering curated multiple-choice questions to sharpen your Linear Algebra knowledge and support exam preparation. Choose a topic below to get started.

1.

The determinant of the matrix whose eigen values are 4, 2, 3 is given by, _______

A. 9
B. 24
C. 5
D. 3
Answer» C. 5
Discussion
2.

Find the trace of the matrix (A = begin{bmatrix}1 & 0 & 6 0 & 5 & 0

A. n0 & 4 & 4 end{bmatrix}. )
B. 0
C. 10
D. 4
E. 1
Answer» C. 10
Discussion
3.

The computation of power of a matrix becomes faster if it is diagonalizable.

A. True
B. False
Answer» B. False
Discussion
4.

If A is diagonalizable then, ____________

A. A<sup>n</sup> = (PDP<sup>-1</sup>)<sup>n</sup> = PD<sup>n</sup>P<sup>n</sup>
B. A<sup>n</sup> = (PDP<sup>-1</sup>)<sup>n</sup> = PD<sup>n</sup>P<sup>1</sup>
C. A<sup>n</sup> = (PDP<sup>-1</sup>)<sup>n</sup> = PD<sup>n</sup>P<sup>-1</sup>
D. A<sup>n</sup> = (PDP<sup>-1</sup>)<sup>n</sup> = PD<sup>n</sup>P
Answer» D. A<sup>n</sup> = (PDP<sup>-1</sup>)<sup>n</sup> = PD<sup>n</sup>P
Discussion
5.

The geometric multiplicity of is its multiplicity as a root of the characteristic polynomial of A, where be the eigen value of A.

A. True
B. False
Answer» C.
Discussion
6.

Which of the following is not a necessary condition for a matrix, say A, to be diagonalizable?

A. A must have n linearly independent eigen vectors
B. All the eigen values of A must be distinct
C. A can be an idempotent matrix
D. A must have n linearly dependent eigen vectors
Answer» E.
Discussion