# 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) $$\begin{bmatrix}1&3&-2\\-1&7&0\\1&0&8\end{bmatrix}$$

Explanation: We know that in a transpose matrix,
The rows and columns get interchanged.
So the transpose of the given matrix will be
$$\begin{bmatrix}1&-1&1\\3&7&0\\-2&0&8\end{bmatrix}$$
.

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) $$\begin{bmatrix}8&-2\\-1&3\end{bmatrix}$$

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) $$\begin{bmatrix}3&12\\2&8\end{bmatrix}$$

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.