Explore topic-wise MCQs in Linear Algebra.

This section includes 7 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.

Determine the algebraic and geometric multiplicity of the following matrix.\(\begin{bmatrix}2 & 4 & -4 \\0 & 4 & 2\\-2 & 4 & 4\end{bmatrix} \)

A. Algebraic multiplicity = 1, Geometric multiplicity = 2
B. Algebraic multiplicity = 1, Geometric multiplicity = 3
C. Algebraic multiplicity = 2, Geometric multiplicity = 2
D. Algebraic multiplicity = 2, Geometric multiplicity = 1
Answer» E.
Discussion
3.

Find the invertible matrix P, by using diagonalization method for the following matrix.A = \(\begin{bmatrix}2 & 0 & 0 \\1 & 2 & 1\\-1 & 0 & 1\end{bmatrix} \)

A. A = \(\begin{bmatrix}-1 & -1 & 0 \\1 & 0 & -1\\-1 & 1 & 1\end{bmatrix} \)
B. A = \(\begin{bmatrix}0 & -1 & 0 \\1 & 0 & -1 \\0 & 1 & 1\end{bmatrix} \)
C. A = \(\begin{bmatrix}0 & 0 & 0\\1 & 1 & -1\\-1 & 0 & 1\end{bmatrix} \)
D. A = \(\begin{bmatrix}1 & 0 & 0\\1 & 0 & -1\\-1 & 0 & 1\end{bmatrix} \)
Answer» C. A = \(\begin{bmatrix}0 & 0 & 0\\1 & 1 & -1\\-1 & 0 & 1\end{bmatrix} \)
Discussion
4.

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

A. True
B. False
Answer» B. False
Discussion
5.

If A is diagonalizable then, ____________

A. An = (PDP-1)n = PDnPn
B. An = (PDP-1)n = PDnP1
C. An = (PDP-1)n = PDnP-1
D. An = (PDP-1)n = PDnP
Answer» D. An = (PDP-1)n = PDnP
Discussion
6.

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

A. True
B. False
Answer» C.
Discussion
7.

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