# Giventhe following matrices:A=begin{bmatrix}1 & 2 &9 -1 & 2 &0 0&0&4 end{bmatrix} B=begin{bmatrix}0 & -1 2 & 6 end{bmatrix} C=begin{bmatrix}2 & 1 0 & 0 end{bmatrix} D=begin{bmatrix}1 2 -4 end{bmatrix}Identify the following:a) A-Bb) B+Cc) C-Dd) B-C

Given the following matrices:
$$A=\begin{bmatrix}1 & 2 &9 \\ -1 & 2 &0 \\ 0&0&4 \end{bmatrix} B=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix} C=\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix} D=\begin{bmatrix}1 \\ 2 \\ -4 \end{bmatrix}$$
Identify the following:
a) A-B
b) B+C
c) C-D
d) B-C

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Tasneem Almond
Step 1
Given:
$$A=\begin{bmatrix}1 & 2 &9 \\ -1 & 2 &0 \\ 0&0&4 \end{bmatrix} B=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix} C=\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix} D=\begin{bmatrix}1 \\ 2 \\ -4 \end{bmatrix}$$
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:
$$A=\begin{bmatrix}1 & 2 &9 \\ -1 & 2 &0 \\ 0&0&4 \end{bmatrix} \Rightarrow \text{order }=3*3$$
$$B=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix} \Rightarrow \text{order }=2*2$$
$$C=\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix} \Rightarrow \text{order }=2*2$$
$$D=\begin{bmatrix}1 \\ 2 \\ -4 \end{bmatrix} \Rightarrow \text{order }=3*1$$
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
$$B+C=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix}+\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix}$$
$$B+C=\begin{bmatrix}0+2 & -1+1 \\ 2+0 & 6+0 \end{bmatrix}$$
$$B+C=\begin{bmatrix}2 &0 \\ 2 & 6 \end{bmatrix}$$
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
$$B-C=\begin{bmatrix}0 & -1 \\ 2 & 6 \end{bmatrix}-\begin{bmatrix}2 & 1 \\ 0 & 0 \end{bmatrix}$$
$$B-C=\begin{bmatrix}0-2 & -1-1 \\ 2-0 & 6-0 \end{bmatrix}$$
$$B-C=\begin{bmatrix}-2 &-2 \\ 2 & 6 \end{bmatrix}$$
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