Linear Algebra Questions and Answers – Types and Properties of Matrices

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This set of Linear Algebra Multiple Choice Questions & Answers (MCQs) focuses on “Types and Properties of Matrices”.

1. Find the transpose of the given Matrix.
\(\begin{bmatrix}1&3&-2\\-1&7&0\\1&0&8\end{bmatrix}\)
a) \(\begin{bmatrix}1&-1&1\\3&7&0\\-2&0&8\end{bmatrix}\)
b) \(\begin{bmatrix}1&1&1\\3&7&0\\-2&0&8\end{bmatrix}\)
c) \(\begin{bmatrix}1&-1&1\\3&7&22\\-2&0&8\end{bmatrix}\)
d) \(\begin{bmatrix}1&3&-2\\-1&7&0\\1&0&8\end{bmatrix}\)
View Answer

Answer: a
Explanation: We know that in a transpose matrix,
The rows and columns get interchanged.
So the transpose of the given matrix will be
\(\begin{bmatrix}1&-1&1\\3&7&0\\-2&0&8\end{bmatrix}\)
.
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2. Which of the following matrix is Skew Symmetric?
a) \(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)
b) \(\begin{bmatrix}0&1\\1&0\end{bmatrix}\)
c) \(\begin{bmatrix}0&3\\-1&9\end{bmatrix}\)
d) \(\begin{bmatrix}8&-2\\-1&3\end{bmatrix}\)
View Answer

Answer: a
Explanation: We know for a Skew Symmetric Matrix,
A=-AT
So for option \(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\),
AT=\(\begin{bmatrix}0&-1\\1&0\end{bmatrix}\)=(-1)\(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)=A.

3. Which of the following matrix are singular?
a) \(\begin{bmatrix}31&12\\26&8\end{bmatrix}\)
b) \(\begin{bmatrix}1&11\\2&8\end{bmatrix}\)
c) \(\begin{bmatrix}13&12\\22&8\end{bmatrix}\)
d) \(\begin{bmatrix}3&12\\2&8\end{bmatrix}\)
View Answer

Answer: d
Explanation: We know that,
A singular matrix is one whose determinant = 0
\(\begin{bmatrix}3&12\\2&8\end{bmatrix}\)
Determinant=24-24=0
Thus it is a singular matrix.

Sanfoundry Global Education & Learning Series – Linear Algebra.

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To practice all areas of Linear Algebra, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn