Matrix Algebra - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2012

Q.11 Let A be the 2 × 2 matrix with elements a₁₁ = a₁₂ = a₂₁ = +1 and a₂₂ = −1. Then the eigenvalues of the matrix A⁹⁹ are

A

1024 and −1024

B

1024√2 and −1024√2

C

4√2 and −4√2

D

512√2 and −512√2

Open complete paper

2

2015 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2015 [Session 1]

Consider the following \(2 \times 2\) matrix \(A\) where two elements are unknown and are marked by \(a\) and \(b\). The eigenvalues of this matrix are -1 and 7. What are the values of \(a\) and \(b\)? \[ A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix} \]

A

\(a = 6, b = 4\)

B

\(a = 4, b = 6\)

C

\(a = 3, b = 5\)

D

\(a = 5, b = 3\)

Open complete paper

3

2015 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2015 [Session 2]

The larger of the two eigenvalues of the matrix \[ \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix} \] is ______.

Check answer

Open complete paper

4

2015 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2015 [Session 2]

Perform the following operations on the matrix \(\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}\).
(i) Add the third row to the second row
(ii) Subtract the third column from the first column.
The determinant of the resultant matrix is _____.

Check answer

Open complete paper

5

2015 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2015 [Session 3]

In the given matrix \(\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}\), one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 are

A

\(\{\alpha(4,2,1)|\alpha \neq 0, \alpha \in \mathbb{R}\}\)

B

\(\{\alpha(-4,2,1)|\alpha \neq 0, \alpha \in \mathbb{R}\}\)

C

\(\{\alpha(\sqrt{2},0,1)|\alpha \neq 0, \alpha \in \mathbb{R}\}\)

D

\(\{\alpha(-\sqrt{2},0,1)|\alpha \neq 0, \alpha \in \mathbb{R}\}\)

Open complete paper

6

2015 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2015 [Session 3]

If the following system has non-trivial solution,
\[ px + qy + rz = 0 \]
\[ qx + ry + pz = 0 \]
\[ rx + py + qz = 0, \]
then which one of the following options is TRUE?

Check answer

Open complete paper

7

2017 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

Let \( c_1, \ldots, c_n \) be scalars, not all zero, such that \( \sum_{i=1}^n c_i a_i = 0 \) where \( a_i \) are column vectors in \( \mathbf{R}^n \). Consider the set of linear equations \( Ax = b \) where \( A = [a_1, \ldots, a_n] \) and \( b = \sum_{i=1}^n a_i \). The set of equations has

A

a unique solution at \(x = J_n \) where \(J_n \) denotes a \(n \)-dimensional vector of all 1

B

no solution

C

infinitely many solutions

D

finitely many solutions

Open complete paper

8

2017 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Computer Science & Information Technology (CS) 2017 [Session 1]

Let \(A\) be \(n \times n\) real valued square symmetric matrix of rank 2 with \(\sum_{i=1}^n \sum_{j=1}^n A_{ij}^2 = 50\). Consider the following statements.
(I) One eigenvalue must be in \([-5, 5]\).
(II) The eigenvalue with the largest magnitude must be strictly greater than 5.
Which of the above statements about eigenvalues of \(A\) is/are necessarily CORRECT?

A

Both (I) and (II)

B

(I) only

C

(II) only

D

Neither (I) nor (II)

Open complete paper