====== Question 4, Exercise 2.1 ======
Solutions of Question 4 of Exercise 2.1 of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 4(i)=====
Find the transpose of the following matrix and identify which one is symmetric and which is skew-symmetric.
$$
A=\left[\begin{array}{ccc}
2 & 0 \\
\sqrt{5} & 6 \\
1 & 9
\end{array}\right]$$

** Solution. **

$$
A^t=\begin{bmatrix}
2 & \sqrt{5} & 1 \\
0 & 6 & 9
\end{bmatrix}$$
=====Question 4(ii)=====
Find the transpose of the following matrix and identify which one is symmetric and which is skew-symmetric.
$$B=\left[\begin{array}{cccc}
1 & 6 & 2 & 0
\end{array}\right] $$

** Solution. **
$$B^t=\left[\begin{array}{c}
1 \\ 6 \\ 2 \\ 0
\end{array}\right] $$


=====Question 4(iii)=====
Find the transpose of the following matrix and identify which one is symmetric and which is skew-symmetric.
$$C=\left[\begin{array}{ll}
2 & 6 \\
9 & 2
\end{array}\right]$$

** Solution. **

$$C^t=\left[\begin{array}{ll}
2 & 9 \\
6 & 2
\end{array}\right]$$
=====Question 4(iv)=====
Find the transpose of the following matrix and identify which one is symmetric and which is skew-symmetric.
$$D=\left[\begin{array}{ccc}
0 & 1 & 9 \\
-1 & 0 & 5 \\
-9 & -5 & 0
\end{array}\right] $$

** Solution. **

$$D^t=\left[\begin{array}{ccc}
0 & -1 & -9 \\
1 & 0 & -5 \\
9 & 5 & 0
\end{array}\right] $$

Since $D^t=-D$, therefore $D$ is skew-symmetric.

=====Question 4(v)=====
Find the transpose of the following matrix and identify which one is symmetric and which is skew-symmetric. 
$$E=\left[\begin{array}{ccc}
3 & -6 & 9 \\
-6 & 2 & 0 \\
9 & 0 & 0
\end{array}\right] $$

** Solution. **

$$E^t=\left[\begin{array}{ccc}
3 & -6 & 9 \\
-6 & 2 & 0 \\
9 & 0 & 0
\end{array}\right] $$

Since $E^t=E$, therefore $E$ is symmetric.

=====Question 4(vi)=====
Find the transpose of the following matrix and identify which one is symmetric and which is skew-symmetric. 
$$F=\left[\begin{array}{ccc}
9 & 0 & 1 \\
0 & 6 & 3 \\
0 & 0 & 1
\end{array}\right]$$


** Solution. **

$$F^t=\left[\begin{array}{ccc}
9 & 0 & 0 \\
0 & 6 & 0 \\
1 & 3 & 1
\end{array}\right]$$


====Go to ====

<text align="left"><btn type="primary">[[math-11-nbf:sol:unit02:ex2-1-p3|< Question 3]]</btn></text>