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

1

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

Mechanical Engineering (ME) 2012

For the matrix A = \begin{bmatrix}5 & 3\\1 & 3\end{bmatrix}, ONE of the normalized eigen vectors is given as

A

\(\begin{pmatrix}1/2\\\sqrt{3}/2\end{pmatrix}\)

B

\(\begin{pmatrix}1/\sqrt{2}\\-1/\sqrt{2}\end{pmatrix}\)

C

\(\begin{pmatrix}3/\sqrt{10}\\-1/\sqrt{10}\end{pmatrix}\)

D

\(\begin{pmatrix}1/\sqrt{5}\\2/\sqrt{5}\end{pmatrix}\)

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2

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

Mechanical Engineering (ME) 2012

The system of algebraic equations given above has
x + 2y + z = 4
2x + y + 2z = 5
x - y + z = 1

A

A unique solution of x = 1, y = 1 and z = 1.

B

only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0).

C

Infinite number of solutions.

D

No feasible solution.

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3

2014 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Mechanical Engineering (ME) 2014 [Session 2]

One of the eigenvectors of the matrix \(\begin{bmatrix} -5 & 2 \\ -9 & 6 \end{bmatrix}\) is

A

\(\begin{bmatrix} -1 \\ 1 \end{bmatrix}\)

B

\(\begin{bmatrix} -2 \\ 9 \end{bmatrix}\)

C

\(\begin{bmatrix} 2 \\ -1 \end{bmatrix}\)

D

\(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\)

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4

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

Mechanical Engineering (ME) 2015 [Session 3]

The lowest eigenvalue of the 2×2 matrix \(\begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}\) is ________

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5

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

Mechanical Engineering (ME) 2015 [Session 3]

For a given matrix P = \(\begin{bmatrix} 4 + 3i & -i \\ i & 4 - 3i \end{bmatrix}\), where i = \(\sqrt{-1}\), the inverse of matrix P is

A

\(\frac{1}{24} \begin{bmatrix} 4 - 3i & i \\ -i & 4 + 3i \end{bmatrix}\)

B

\(\frac{1}{25} \begin{bmatrix} i & 4 - 3i \\ 4 + 3i & -i \end{bmatrix}\)

C

\(\frac{1}{24} \begin{bmatrix} 4 + 3i & -i \\ i & 4 - 3i \end{bmatrix}\)

D

\(\frac{1}{25} \begin{bmatrix} 4 + 3i & -i \\ i & 4 - 3i \end{bmatrix}\)

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6

2019 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Mechanical Engineering (ME) 2019 [Session 2]

In matrix equation [A]{X}={R}, [A]=[4 8 4; 8 16 -4; 4 -4 15], {X}={2;1;4} and {R}={32;16;64}. One of the eigenvalues of matrix [A] is

A

4

B

8

C

15

D

16

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