OlmekinjP

2021-01-04

Matrix multiplication is pretty tough- so i will cover that in class. In the meantime , compute the following if

$A=\left[\begin{array}{ccc}2& 1& 1\\ -1& -1& 4\end{array}\right],B=\left[\begin{array}{cc}0& 2\\ -4& 1\\ 2& -3\end{array}\right],C=\left[\begin{array}{cc}6& -1\\ 3& 0\\ -2& 5\end{array}\right],D=\left[\begin{array}{ccc}2& -3& 4\\ -3& 1& -2\end{array}\right]$

If the operation is not possible , write NOT POSSIBLE and be able to explain why

a)A+B

b)B+C

c)2A

If the operation is not possible , write NOT POSSIBLE and be able to explain why

a)A+B

b)B+C

c)2A

Obiajulu

Skilled2021-01-05Added 98 answers

Step 1

$\text{Given :}A=\left[\begin{array}{ccc}2& 1& 1\\ -1& -1& 4\end{array}\right],B=\left[\begin{array}{cc}0& 2\\ -4& 1\\ 2& -3\end{array}\right],C=\left[\begin{array}{cc}6& -1\\ 3& 0\\ -2& 5\end{array}\right],D=\left[\begin{array}{ccc}2& -3& 4\\ -3& 1& -2\end{array}\right]$

Solution for question a:

To compute A+B:

Note that two matrices may be added if and only if they have the same dimension, that is, they must have the same number of rows and columns.

Here, Dimension of$A=2\times 3$

And, Dimension of$B=3\times 2$

Matrix A and B do not have the same dimension. Hence, matrix A and B cannot be added.

Therefore it is not possible to perform A+B.

Step 2

Solution for question b:

Here,

Dimension of matrix$B=3\times 2$

Dimension of matrix$C=3\times 2$

Both matrices B and C have the same dimension. Hence, matrix B and C can be added.

Further,

$B+C=\left[\begin{array}{cc}0& 2\\ -4& 1\\ 2& -3\end{array}\right]+\left[\begin{array}{cc}6& -1\\ 3& 0\\ -2& 5\end{array}\right]$

$=\left[\begin{array}{cc}0+6& 2+(-1)\\ -4+3& 1+0\\ 2+(-2)& (-3)+5\end{array}\right]$

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

Therefore,

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

Step 3

Solution for question c:

To compute 2A multiply each entry of the matrix A by 2.

$2A=2\left[\begin{array}{ccc}2& 1& 1\\ -1& -1& 4\end{array}\right]$

$=\left[\begin{array}{ccc}4& 2& 2\\ -2& -2& 8\end{array}\right]$

therefore,

$2A=\left[\begin{array}{ccc}4& 2& 2\\ -2& -2& 8\end{array}\right]$

Solution for question a:

To compute A+B:

Note that two matrices may be added if and only if they have the same dimension, that is, they must have the same number of rows and columns.

Here, Dimension of

And, Dimension of

Matrix A and B do not have the same dimension. Hence, matrix A and B cannot be added.

Therefore it is not possible to perform A+B.

Step 2

Solution for question b:

Here,

Dimension of matrix

Dimension of matrix

Both matrices B and C have the same dimension. Hence, matrix B and C can be added.

Further,

Therefore,

Step 3

Solution for question c:

To compute 2A multiply each entry of the matrix A by 2.

therefore,

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

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