Exercise 2.1 (Solutions)
The solutions of the Exercise 2.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to order, different type of matrices and transpose of matrix.
Question 1. Find the order of the following matrix:
(i) $A=\left[\begin{array}{lll}1 & 3 & 0 \\ 2 & 0 & 1\end{array}\right]$
(ii) $B=\left[\begin{array}{ll}1 & 2 \\ 2 & 3 \\ 3 & 4\end{array}\right]$
(iii) $C=\left[\begin{array}{l}1 \\ 6 \\ 9\end{array}\right]$
(iv) $D=\left[\begin{array}{llll}2 & 1 & 6 & 8\end{array}\right]$
(v) $E=[3]$
(vi) $F=\left[\begin{array}{ll}3 & 6 \\ 9 & 2\end{array}\right]$
Solution: Question 1
Question 2. Identify the following matrices as square matrix, rectangular matrix, row matrix or column matrix.
(i) $\quad A=\left[\begin{array}{lll}3 & 6 & 2 \\ 2 & 1 & 9\end{array}\right]$
(ii) $B=\left[\begin{array}{ll}\frac{1}{3} & 1 \\ 2 & 6\end{array}\right]$
(iii) $C=\left[\begin{array}{l}3 \\ 2 \\ 8\end{array}\right]$
(iv) $D=\left[\begin{array}{lll}1 & 6 & 9 \\ 2 & 0 & 1 \\ 3 & 1 & 2\end{array}\right]$
(v) $E=\left[\begin{array}{lll}2 & 0 & 1\end{array}\right]$
(vi) $F=[16]$
Solution:Question 2
Question 3. Identify the diagonal matrix, scalar matrix, identity matrix, lower triangular matrix, upper triangular matrix.
$A=\left[\begin{array}{lll} 3 & 0 & 0 \\ 0 & 1 & 0 \\ 2 & 6 & 0 \end{array}\right] ;$
$B=\left[\begin{array}{lll} -6 & 0 & 0 \\ 0 & -6 & 0 \\ 0 & 0 & -6 \end{array}\right] ;$
$C=\left[\begin{array}{ll} 1 & 0 \\ 2 & 0 \end{array}\right] ; $
$D=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] ;$
$E=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 0 \end{array}\right] ;$
$F=\left[\begin{array}{lll}\sqrt{3} & 1 & 2 \\0 & 0 & 6 \\0 & 0 & 1 \end{array}\right] ; $
$G=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right] ;$
$H=\left[\begin{array}{ll} 2 & 0 \\ 0 & 2\end{array}\right]$
Solution:Question 3
Question 4. Find the transpose of the following matrices and identify which one of them are symmetric and which are skew-symmetric.
$A=\left[\begin{array}{ll}
2 & 0
\sqrt{5} & 6
1 & 9
\end{array}\right] ; $
$B=\left[\begin{array}{llll}1 & 6 & 2 & 0 \end{array}\right] ; $
$C=\left[\begin{array}{ll} 2 & 6 \\ 9 & 2 \end{array}\right] ; $
$D=\left[\begin{array}{lll} 0 & 1 & 9 \\ -1 & 0 & 5 \\ -9 & -5 & 0 \end{array}\right] ;$
$E=\left[\begin{array}{lll} 3 & -6 & 9 \\-6 & 2 & 0 \\9 & 0 & 0\end{array}\right] ;$
$F=\left[\begin{array}{lll}9 & 0 & 1 \\0 & 6 & 3 \\0 & 0 & 1\end{array}\right]$
Solution:Question 4