Given the following matrices: A=[129−120004]B=[0−126]C=[2100]D=[12−4] Identify the following: a) A-B b) B+C c) C-D d)...

Step 1
Given:
$A=\left[\begin{array}{ccc}1& 2& 9\\ -1& 2& 0\\ 0& 0& 4\end{array}\right]B=\left[\begin{array}{cc}0& -1\\ 2& 6\end{array}\right]C=\left[\begin{array}{cc}2& 1\\ 0& 0\end{array}\right]D=\left[\begin{array}{c}1\\ 2\\ -4\end{array}\right]$
a) A-B
b) B+C
c) C-D
d) B-C
Step 2
Concept:
The number of rows and columns of the matrix is known as its order
Step 3
Solution:
Order of the given matrices:
$A=\left[\begin{array}{ccc}1& 2& 9\\ -1& 2& 0\\ 0& 0& 4\end{array}\right]\Rightarrow \text{order }=3\ast 3$
$B=\left[\begin{array}{cc}0& -1\\ 2& 6\end{array}\right]\Rightarrow \text{order }=2\ast 2$
$C=\left[\begin{array}{cc}2& 1\\ 0& 0\end{array}\right]\Rightarrow \text{order }=2\ast 2$
$D=\left[\begin{array}{c}1\\ 2\\ -4\end{array}\right]\Rightarrow \text{order }=3\ast 1$
Step 4
For A-B
The order of Matrix A and B are different. Hence, we can’t do addition and subtraction in these matrices
Step 5
For B+C
The order of Matrix B and C are the same. Hence, we can do addition and subtraction in these matrices
$B+C=\left[\begin{array}{cc}0& -1\\ 2& 6\end{array}\right]+\left[\begin{array}{cc}2& 1\\ 0& 0\end{array}\right]$
$B+C=\left[\begin{array}{cc}0+2& -1+1\\ 2+0& 6+0\end{array}\right]$
$B+C=\left[\begin{array}{cc}2& 0\\ 2& 6\end{array}\right]$
Step 6
For C-D
The order of Matrix C and D are different. Hence, we can’t do addition and subtraction in these matrices
Step 7
For B-C
The order of Matrix B and C are the same. Hence, we can do addition and subtraction in these matrices
$B-C=\left[\begin{array}{cc}0& -1\\ 2& 6\end{array}\right]-\left[\begin{array}{cc}2& 1\\ 0& 0\end{array}\right]$
$B-C=\left[\begin{array}{cc}0-2& -1-1\\ 2-0& 6-0\end{array}\right]$
$B-C=\left[\begin{array}{cc}-2& -2\\ 2& 6\end{array}\right]$

Answer is given below (on video)