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

1

2007 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Aerospace Engineering (AE) 2007

Let P and Q be two square matrices of same size. Consider the following statements
(i) PQ = 0 implies P = 0 or Q = 0 or both
(ii) PQ = I^2 implies P = Q^{-1}
(iii) (P+Q)^2 = P^2 + 2PQ + Q^2
(iv) (P-Q)^2 = P^2 - 2PQ + Q^2
where I is the identity matrix. Which of the following statements is correct?

A

(i), (ii) and (iii) are false, but (iv) is true

B

(i), (ii) and (iv) are false, but (iii) is true

C

(iii), (iii) and (iv) are false, but (i) is true

D

(i), (iii) and (iv) are false, but (ii) is true

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2

2007 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Aerospace Engineering (AE) 2007

Let a system of linear equations be as follows:
\(x - y + 2z = 0\)
\(2x + 3y - z = 0\)
\(2x - 2y + 4z = 0\)
This system of equations has

A

No non-trivial solution

B

Infinite number of non-trivial solutions

C

An unique non-trivial solution

D

Two non-trivial solutions

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3

2008 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Aerospace Engineering (AE) 2008

Which of the following equations is a LINEAR ordinary differential equation?

A

\(\frac{d^2 y}{dx^2} + \frac{dy}{dx} + 2y^2 = 0 \)

B

\(\frac{d^2 y}{dx^2} + y \frac{dy}{dx} + 2y = 0 \)

C

\(\frac{d^2 y}{dx^2} + x \frac{dy}{dx} + 2y = 0 \)

D

\(\left( \frac{dy}{dx} \right)^2 + \frac{dy}{dx} + 2y = 0 \)

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4

2010 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Aerospace Engineering (AE) 2010

The eigen-values of a real symmetric matrix are always

A

positive

B

imaginary

C

real

D

complex conjugate pairs

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5

2011 · General Aptitude (GA) · General Aptitude · Matrix Algebra

Aerospace Engineering (AE) 2011

Two simultaneous equations given by \(y = \pi + x\) and \(y = x - \pi\) have

A

a unique solution

B

infinitely many solutions

C

no solution

D

a finite number of multiple solutions

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6

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

Aerospace Engineering (AE) 2015

The 2-D stress state at a point \( P \) in the \( x-y \) coordinate system is \( \begin{bmatrix} 60 & 50 \\ 50 & -40 \end{bmatrix} \) MPa. The magnitude of the tangential stress (in MPa) on a surface normal to the \( x \)-axis at \( P \) is ______.

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