Explore topic-wise MCQs in Linear Algebra.

This section includes 8 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 sum of two skew-symmetric matrices is also a skew-symmetric matrix.

A. False
B. True
Answer» C.
Discussion
2.

Which of the following is known as Hadamard matrix?

A. ( begin{bmatrix}1 & 0 & 1 & 0 0 & 1 & 0 & 1 1 & 0 & 1 & 0 0 & 1 & 0 & 1 end{bmatrix} )
B. ( begin{bmatrix}1 & -1 & 1 & -1 1 & -1 & 1 & -1 1 & -1 & 1 & -1 1 & -1 & 1 & -1 end{bmatrix} )
C. ( begin{bmatrix}1 & 1 & 1 & 1 1 & 1 & 1 & 1 1 & 1 & 1 & 1 1 & 1 & 1 & 1 end{bmatrix} )
D. ( begin{bmatrix}0 & 0 & 0 & 0 0 & 1 & 1 & 0 0 & 1 & 1 & 0 0 & 0 & 0 & 0 end{bmatrix} )
Answer» C. ( begin{bmatrix}1 & 1 & 1 & 1 1 & 1 & 1 & 1 1 & 1 & 1 & 1 1 & 1 & 1 & 1 end{bmatrix} )
Discussion
3.

Find the symmetric matrix for the given quadratic form, (Q = 2x_1^2 + 2x_2^2 + 5x_3^2 3x_1 x_2+7x_3 x_1. )

A. ( begin{bmatrix} 1 & frac{-7}{2} & frac{3}{2} frac{-7}{2} & 2 & 0 frac{3}{2} & 0 & frac{5}{2} end{bmatrix} )
B. ( begin{bmatrix} 1 & frac{-3}{2} & frac{7}{2} frac{-3}{2} & 2 & 0 frac{7}{2} & 0 & frac{5}{2} end{bmatrix} )
C. ( begin{bmatrix} 1 & frac{3}{2} & frac{-7}{2} frac{3}{2} & 2 & 0 - frac{7}{2} & 0 & frac{5}{2} end{bmatrix} )
D. ( begin{bmatrix} 1 & frac{-3}{2} & frac{7}{2} frac{-3}{2} & 2 & 0 frac{7}{2} & 0 & 5 end{bmatrix} )
Answer» C. ( begin{bmatrix} 1 & frac{3}{2} & frac{-7}{2} frac{3}{2} & 2 & 0 - frac{7}{2} & 0 & frac{5}{2} end{bmatrix} )
Discussion
4.

Every Identity matrix is an orthogonal matrix.

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

Which of the following is known as the reversal rule?

A. (AB)<sup>-1</sup> = B<sup>-1</sup>A<sup>-1</sup>
B. (AB)<sup>-1</sup> = A<sup>-1</sup> B<sup>-1</sup>
C. (BA)<sup>-1</sup> = B<sup>-1</sup> A<sup>-1</sup>
D. (BA)<sup>-1</sup> = B<sup>-1</sup> A
Answer» B. (AB)<sup>-1</sup> = A<sup>-1</sup> B<sup>-1</sup>
Discussion
6.

The matrix which remains unchanged under transposition is known as skew symmetric matrix.

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

Which among the following is listed under the law of transposes?

A. (A<sup>T</sup>)<sup>T</sup> = A<sup>I</sup>
B. (A*)* = A*
C. (cA)<sup>T</sup> = cA<sup>T</sup>
D. (AB)<sup>T</sup> = A<sup>T</sup>B<sup>T</sup>
Answer» D. (AB)<sup>T</sup> = A<sup>T</sup>B<sup>T</sup>
Discussion
8.

Who introduced the term matrix?

A. James Sylvester
B. Arthur Cayley
C. Girolamo Cardano
D. Paul Erdos
Answer» B. Arthur Cayley
Discussion