Given the matrices $A$ and $B$, find the matrix product $A B$.
-$A=\left[\begin{array}{rrr}1 & 3 & -3 \ 2 & 0 & 3\end{array}\right], B=\left[\begin{array}{rr}3 & 0 \ -3 & 1 \ 0 & 3\end{array}\right]$ Find $A B$.
A)$\left[\begin{array}{rr}-6 & -6 \ 6 & 9\end{array}\right]$
B)AB is not defined.
C)$$\left[\begin{array}{rrr}
3 & -9 & 0 \
0 & 0 & 9
\end{array}\right]$$
D) $\left[\begin{array}{rr}-6 & -6 \ 9 & 6\end{array}\right]$

Question

Quizplus · Accepted Answer

The number of columns in $A$ must equal the number of rows in $B$ for the matrix product $A B$ to be defined. Since $A$ has 3 columns and $B$ has 2 rows, the matrix product $A B$ is defined.To find the matrix product $A B$, we multiply each element in the first row of $A$ by each element in the first column of $B$, and then add the products. We do this for each row in $A$ and each column in $B$.$A B=\left[\begin{array}{rrr}1 & 3 & -3 \ 2 & 0 & 3\end{array}\right]\left[\begin{array}{rr}3 & 0 \ -3 & 1 \ 0 & 3\end{array}\right]$$=\left[\begin{array}{rr}1(3)+3(-3)+(-3)(0) & 1(0)+3(1)+(-3)(3) \ 2(3)+0(-3)+3(0) & 2(0)+0(1)+3(3)\end{array}\right]$$=\left[\begin{array}{rr}-6 & -6 \ 6 & 9\end{array}\right]$Therefore, the matrix product $A B$ is $\left[\begin{array}{rr}-6 & -6 \ 6 & 9\end{array}\right]$.

Given the Matrices AAA And BBB , Find the Matrix Product ABA BAB

Given the Matrices $A$ And $B$ , Find the Matrix Product $A B$