# Use the graphing calculator to solve if possible A=begin{bmatrix}1 & 0&5 1 & -5&70&3&-4 end{bmatrix} B=begin{bmatrix}3 & -5&3 2&3&14&1&-3end{bmatrix} C=begin{bmatrix}5 & 2&3 2& -1&0 end{bmatrix} D=begin{bmatrix}5 -34 end{bmatrix} Find the value in row 2 column 3 of AB-3B

Question
Matrices
Use the graphing calculator to solve if possible
A=\begin{bmatrix}1 & 0&5 \\1 & -5&7\\0&3&-4 \end{bmatrix}\\ B=\begin{bmatrix}3 & -5&3 \\2&3&1\\4&1&-3\end{bmatrix}\\ C=\begin{bmatrix}5 & 2&3 \\2& -1&0 \end{bmatrix}\\ D=\begin{bmatrix}5 \\-3\\4 \end{bmatrix}
Find the value in row 2 column 3 of AB-3B

2021-03-10
Step 1
Given:
The given matrices are
$$A=\begin{bmatrix}1 & 0&5 \\1 & -5&7\\0&3&-4 \end{bmatrix}$$
$$B=\begin{bmatrix}3 & -5&3 \\2&3&1\\4&1&-3\end{bmatrix}$$
$$C=\begin{bmatrix}5 & 2&3 \\2& -1&0 \end{bmatrix}$$
$$D=\begin{bmatrix}5 \\-3\\4 \end{bmatrix}$$
To find:
The value in row 2 column 3 of AB-3B.
Step 2
The matrices are $$A=\begin{bmatrix}1 & 0&5 \\1 & -5&7\\0&3&-4 \end{bmatrix},B=\begin{bmatrix}3 & -5&3 \\2&3&1\\4&1&-3\end{bmatrix}$$
Now,
$$AB-3B=\begin{bmatrix}1 & 0&5 \\1 & -5&7\\0&3&-4 \end{bmatrix}\begin{bmatrix}3 & -5&3 \\2&3&1\\4&1&-3\end{bmatrix}-3\begin{bmatrix}3 & -5&3 \\2&3&1\\4&1&-3\end{bmatrix}$$
$$AB-3B=\begin{bmatrix}23 & 0&-12 \\21 & -13&-23\\-10&5&15 \end{bmatrix}-\begin{bmatrix}9 & -15&9 \\6&9&3\\12&3&-9\end{bmatrix}$$
$$AB-3B=\begin{bmatrix}14 & 15&-21 \\ 15&-22&-26\\-22&2&24\end{bmatrix}$$
The value in row 2 column 3 of AB-3B is -26.

### Relevant Questions

If $$A=\begin{bmatrix}1 & 1 \\3 & 4 \end{bmatrix} , B=\begin{bmatrix}2 \\1 \end{bmatrix} ,C=\begin{bmatrix}-7 & 1 \\0 & 4 \end{bmatrix},D=\begin{bmatrix}3 & 2 & 1 \end{bmatrix} \text{ and } E=\begin{bmatrix}2 & 3&4 \\1 & 2&-1 \end{bmatrix}$$
Find , if possible,
a) A+B , C-A and D-E b)AB, BA , CA , AC , DA , DB , BD , EB , BE and AE c) 7C , -3D and KE
compute the indicated matrices (if possible). B - C
Let
$$A=\begin{bmatrix}3 & 0 \\-1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2&1 \\0 & 2&3 \end{bmatrix} , C=\begin{bmatrix}1 & 2 \\3 & 4\\5&6 \end{bmatrix}, D=\begin{bmatrix}0 & -3 \\-2 & 1 \end{bmatrix},E=\begin{bmatrix}4 & 2 \end{bmatrix},F=\begin{bmatrix}-1 \\2 \end{bmatrix}$$
If possible , find 2A-4B
$$A=\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix} , B=\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}$$
a. $$\begin{bmatrix}-30 & 42 & -24 \\ 18 & 14 & -10 \end{bmatrix}$$
b. not possible
c. $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}$$
d. $$\begin{bmatrix} -9 & 13 & -9 \\ 6 & 1 & -3 \end{bmatrix}$$
c. $$\begin{bmatrix} 18 & -22 & 0 \\ -6 & -34 & 6 \end{bmatrix}$$
Enter the expression that would produce the answer (do include the answer) for row 1 column 1 of the multiplied matrix $$A \cdot B$$:
List the expression in order with the original values using $$\cdot$$ for multiplication.
then find $$A \cdot B$$
If $$A=\begin{bmatrix}3 & 7 \\2 & 4 \end{bmatrix} \text{ and } B=\begin{bmatrix}-3 & 6 \\4 & -2 \end{bmatrix}$$
Find if possible the matrices:
a. AB b. BA.
$$A=\begin{bmatrix}1 & -1&4 \\4 & -1&3\\2&0&-2 \end{bmatrix} , B=\begin{bmatrix}1 & 1&0 \\1 & 2&4\\1&-1&3 \end{bmatrix}$$
find which of the given matrices are nonsingular.
a) $$\begin{bmatrix}1 & 2 &-3 \\-1 & 2&3 \\ 0 &8&0 \end{bmatrix}$$
b)$$\begin{bmatrix}1 & 2 &-3 \\-1 & 2&3 \\ 0 &1&1 \end{bmatrix}$$
c) $$\begin{bmatrix}1 & 1 &2 \\-1 & 3&4 \\ -5 &7&8 \end{bmatrix}$$
d) $$\begin{bmatrix}1 & 1 &4&-1 \\1 & 2&3&2 \\ -1 &3&2&1\\-2&6&12&-4 \end{bmatrix}$$
Compute the product AB by the definition of the product of​ matrices, where $$Ab_1 \text{ and } Ab_2$$ are computed​ separately, and by the​ row-column rule for computing AB.
$$A=\begin{bmatrix}-1 & 2 \\2 & 5\\5&-3 \end{bmatrix} , B=\begin{bmatrix}4 & -1 \\-2 & 4 \end{bmatrix}$$
Determine the product AB
AB=?
Consider the following two matrices. Why can't the product of the following two matrices be found? $$A=\begin{bmatrix}-1 & 2&3 \\4 & 0&5 \end{bmatrix} \text{ and } B=\begin{bmatrix}5 & 2 \\7 & -8 \end{bmatrix}$$
$$A=\begin{bmatrix}2& 1&1 \\-1 & -1&4 \end{bmatrix} B=\begin{bmatrix}0& 2 \\-4 & 1\\2 & -3 \end{bmatrix} C=\begin{bmatrix}6& -1 \\3 & 0\\-2 & 5 \end{bmatrix} D=\begin{bmatrix}2& -3&4 \\-3 & 1&-2 \end{bmatrix}$$
a)$$A-3D$$
b)$$B+\frac{1}{2}$$
c) $$C+ \frac{1}{2}B$$
$$A=\begin{bmatrix}3 & 0 \\-1 & 5 \end{bmatrix} , B=\begin{bmatrix}4 & -2&1 \\0 & 2&3 \end{bmatrix} , C=\begin{bmatrix}1& 2 \\3 & 4\\5&6 \end{bmatrix} , D=\begin{bmatrix}0 & -3 \\-2 & 1 \end{bmatrix} , E=\begin{bmatrix}4 & 2 \end{bmatrix} ,F=\begin{bmatrix}-1 \\2 \end{bmatrix}$$