Question

Given the matrices: 1 2 A= 1 -1 2 1 1 B= 3 4 Calculate AB: C11 C12 [2.1] х 1 2 3 4 C21 C22 C11 = C12 = -2 C22 - C215 DONE​

Answer 1

Explanation:

c12: -2

c22: 8

d11: 5

d21: 11

Are the products equal? Does AB = BA?

No

Answer 2

`\:c_(11)=-2,\:\:\:c_(12)=-2`

`\:c_(21)=5,\:\:\:c_(22)=8`

Explanation:

Given the matrices

`A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}`

`B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}`

Calculating AB:

`\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}* \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_(11)&c_(12)\\ \:\:\:c_(21)&c_(22)\end{pmatrix}`

Multiply the rows of the first matrix by the columns of the second matrix

`=\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}`

`=\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}`

Hence,

`\begin{pmatrix}c_(11)&c_(12)\\ \:\:\:c_(21)&c_(22)\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}`

Therefore,

`\:c_(11)=-2,\:\:\:c_(12)=-2`

`\:c_(21)=5,\:\:\:c_(22)=8`