Matrix Multiplication Quiz

let $A$ be a matrix of $1$ x $5$ and $B$ be matrix of $5$ x $3$.

$A=\begin{bmatrix} 0.6 &-15 &2&5&98\end{bmatrix}$

$B=\begin{bmatrix} 2&2&-4\\ 9 &-14 &0\\13&-0.5&44\\1&9&4\\0&0&5\end{bmatrix}$

Notice that $A$ is actually a row vector! A matrix with only one row or one column is a vector

• A matrix with only one row is a row vector
• A matrix with only one column is a column vector

If $C=A$x$B$,

(a) How many rows will $C$ have?

(b) How many columns will $C$ have?

(c) What will be the value of $c_{13}$?

If $C=B$x$A$,

(d) What will be the value of $c_{13}$?

Notice that in this quiz, we multiplied a vector by a matrix, which resulted in another vector.
Essentially what happened was that our original vector, $\begin{bmatrix} 0.6 &-15 &2&5&98\end{bmatrix}$, went through a linear transformation and transformed into another vector with the use of the transformation matrix $\begin{bmatrix} 2&2&-4\\ 9 &-14 &0\\13&-0.5&44\\1&9&4\\0&0&5\end{bmatrix}$ .

All this in the next set of videos.

Remember: if you are having issues with the workspace, reset your data.