Find the product. $$\left[ \begin{array} { c c c c }
2 & 1 & 0 & 0 \
- 1 & 2 & 0 & - 4 \
0 & 0 & 2 & 0 \
0 & 4 & 0 & 2
\end{array} \right] \left[ \begin{array} { c }
5 \
3 \
- 3 \
- 5
\end{array} \right]$$
A) $$\left[ \begin{array} { c }
13 \
21 \
- 6 \
2
\end{array} \right]$$
B) $$\left[ \begin{array} { c c }
13 & 21 \
- 6 & 2
\end{array} \right]$$
C) $$\left[ \begin{array} { c }
2 \
- 6 \
21 \
13
\end{array} \right]$$
D) $$\left[ \begin{array} { l l l l }
13 & 21 & - 6 & 2
\end{array} \right]$$
E)cannot multiply

Question

Find the product.​ $$\left[ \begin{array} { c c c c } 
2 & 1 & 0 & 0 \
- 1 & 2 & 0 & - 4 \
0 & 0 & 2 & 0 \
0 & 4 & 0 & 2
\end{array} \right] \left[ \begin{array} { c } 
5 \
3 \
- 3 \
- 5
\end{array} \right]$$ ​
A) $$\left[ \begin{array} { c } 
13 \
21 \
- 6 \
2
\end{array} \right]$$ ​
B) $$\left[ \begin{array} { c c } 
13 & 21 \
- 6 & 2
\end{array} \right]$$ ​
C) $$\left[ \begin{array} { c } 
2 \
- 6 \
21 \
13
\end{array} \right]$$ ​
D) $$\left[ \begin{array} { l l l l } 
13 & 21 & - 6 & 2
\end{array} \right]$$ ​
E)cannot multiply ​

Quizplus · Accepted Answer

To find the product of a matrix and a vector, multiply each row of the matrix by the corresponding entries of the vector and sum the results. For the given matrices, the calculations are as follows: 1. For the first row: $2*5 + 1*3 + 0*(-3) + 0*(-5) = 10 + 3 = 13$2. For the second row: $-1*5 + 2*3 + 0*(-3) - 4*(-5) = -5 + 6 + 20 = 21$3. For the third row: $0*5 + 0*3 + 2*(-3) + 0*(-5) = -6$4. For the fourth row: $0*5 + 4*3 + 0*(-3) + 2*(-5) = 12 - 10 = 2$Thus, the product is a column vector $\left[ \begin{array} { c } 13 \ 21 \ -6 \ 2 \end{array} \right]$.

Find the Product ​ A) [1321−62]\left[ \begin{array} { c } 13 \\21 \\- 6 \\2\end{array} \right]​1321−62​​

Find the Product
A) $\left[ \begin{array} { c } 13 \\21 \\- 6 \\2\end{array} \right]$