Questions: Let C= [2 2 -6; 5 7 -6; 4 1 6] and D= [5 7 0; 3 6 5; 4 -2 5] Find DC if it is defined. Otherwise, click on "Undefined". DC=

Transcript text: Let $C=\left[\begin{array}{rrr}2 & 2 & -6 \\ 5 & 7 & -6 \\ 4 & 1 & 6\end{array}\right]$ and $D=\left[\begin{array}{ccc}5 & 7 & 0 \\ 3 & 6 & 5 \\ 4 & -2 & 5\end{array}\right]$ Find $D C$ if it is defined. Otherwise, click on "Undefined". \[ D C= \] $\square$

Solution

Solution Steps

Step 1: Verify if multiplication is defined

Since the number of columns in matrix $A$ ($n=3$) equals the number of rows in matrix $B$ ($p=3$), the multiplication is defined.

Step 2: Perform the multiplication

The product $AB$ is calculated using the formula: \[ c_{ij} = \sum_{k=1}^{n} a_{ik}b_{kj} \] where $c_{ij}$ is the element in the $i$th row and $j$th column of the resulting matrix $C$, $a_{ik}$ is the element in the $i$th row and $k$th column of matrix $A$, and $b_{kj}$ is the element in the $k$th row and $j$th column of matrix $B$.

Step 3: Construct the resulting matrix $C$

After performing the calculations, the resulting matrix $C$ is: [45, 59, -72] [56, 53, -24] [18, -1, 18]