Question

Care este rezultatului inmultirii matriciei A cu matricia B, unde A= (1 1 2
2 2 4
2 1 2) , iar B=(1
0
3)

Answer 1

A · B = $\left[\begin{array}{ccc}1&1&2\\2&2&4\\2&1&2\end{array}\right]$ · $\left[\begin{array}{ccc}1\\0\\3\end{array}\right]$

= $\left[\begin{array}{ccc}7\\14\\8\end{array}\right]$

Answer 2

$\displaystyle \mathtt{A= \mathtt{\left(\begin{array}{ccc}\mathtt1&\mathtt1&\mathtt2\\\mathtt2&\mathtt2&\mathtt4\\\mathtt2&\mathtt1&\mathtt2\end{array}\right)};~B=\left(\begin{array}{ccc}\mathtt1\\\mathtt0\\\mathtt3\end{array}\right)~~~~~~~~~~~~~~~~~~~~~~A \cdot B=?}$

$\displaystyle \mathtt{A\cdot B=\left(\begin{array}{ccc}\mathtt1&\mathtt1&\mathtt2\\\mathtt2&\mathtt2&\mathtt4\\\mathtt2&\mathtt1&\mathtt2\end{array}\right)\cdot\left(\begin{array}{ccc}\mathtt1\\\mathtt0\\\mathtt3\end{array}\right)=\left(\begin{array}{ccc}\mathtt{1 \cdot 1+1\cdot0+2 \cdot 3}\\\mathtt{2\cdot1+2\cdot0+4\cdot3}\\\mathtt{2\cdot1+1\cdot0+2\cdot3}\end{array}\right)=}$

$\displaystyle \mathtt{=\left(\begin{array}{ccc}\mathtt{1+0+6}\\\mathtt{2+0+12}\\\mathtt{2+0+6}\end{array}\right)= \left(\begin{array}{ccc}\mathtt7\\\mathtt{14}\\\mathtt8\end{array}\right)} \\ \\ \\\mathtt{A\cdot B=\left(\begin{array}{ccc}\mathtt7\\\mathtt{14}\\\mathtt8\end{array}\right)}$