vestirme4

2021-02-05

Given the following matrices:

Identify the following:

a) A-B

b) B+C

c) C-D

d) B-C

Tasneem Almond

Skilled2021-02-06Added 91 answers

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

$B-C=\left[\begin{array}{cc}0& -1\\ 2& 6\end{array}\right]-\left[\begin{array}{cc}2& 1\\ 0& 0\end{array}\right]$

$B-C=\left[\begin{array}{cc}0-2& -1-1\\ 2-0& 6-0\end{array}\right]$

$B-C=\left[\begin{array}{cc}-2& -2\\ 2& 6\end{array}\right]$

Given:

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:

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

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

Jeffrey Jordon

Expert2022-01-22Added 2575 answers

Answer is given below (on video)