Find the product. 0.2⎡⎣⎢100.25−12⎤⎦⎥ Complete the matrix that represents the product. (2 points) 0.2⎡⎣⎢100.25−12⎤⎦⎥= $$

Answer 1

To find the product of \( 0.2 \) and the matrix \( \begin{bmatrix} 100 & 0.25 \ -1 & 2 \end{bmatrix} \), we simply multiply each element of the matrix by \( 0.2 \).

Let's perform the multiplication:

\[ 0.2 \cdot \begin{bmatrix} 100 & 0.25 \ -1 & 2 \end{bmatrix} = \begin{bmatrix} 0.2 \cdot 100 & 0.2 \cdot 0.25 \ 0.2 \cdot -1 & 0.2 \cdot 2 \end{bmatrix} \]

Calculating each element:

1. \( 0.2 \cdot 100 = 20 \)
2. \( 0.2 \cdot 0.25 = 0.05 \)
3. \( 0.2 \cdot -1 = -0.2 \)
4. \( 0.2 \cdot 2 = 0.4 \)

Putting this together, the resulting matrix will be:

\[ 0.2 \cdot \begin{bmatrix} 100 & 0.25 \ -1 & 2 \end{bmatrix} = \begin{bmatrix} 20 & 0.05 \ -0.2 & 0.4 \end{bmatrix} \]

Thus, the complete product is

\[ \begin{bmatrix} 20 & 0.05 \ -0.2 & 0.4 \end{bmatrix}. \]