Question

calculate this reflection of the triangle:
\\( \

$$\begin{bmatrix} 1 & 0 \\\\ 0 & -1 \\end{bmatrix}$$

\times \

$$\begin{bmatrix} 0 & 3 & 0 \\\\ 0 & 0 & 2 \\end{bmatrix}$$

= \

$$\begin{bmatrix} 0 & a & b \\\\ 0 & c & d \\end{bmatrix}$$

\\)

Explanation:

Step1: Matrix multiplication formula

For two matrices \(A =

$$\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{bmatrix}$$

\) and \(B=

$$\begin{bmatrix}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\end{bmatrix}$$

\), the product \(AB=

$$\begin{bmatrix}a_{11}b_{11}+a_{12}b_{21}&a_{11}b_{12}+a_{12}b_{22}&a_{11}b_{13}+a_{12}b_{23}\\a_{21}b_{11}+a_{22}b_{21}&a_{21}b_{12}+a_{22}b_{22}&a_{21}b_{13}+a_{22}b_{23}\end{bmatrix}$$

\)

Step2: Calculate element \(a\)

\(a = 1\times3+0\times0=3\)

Step3: Calculate element \(b\)

\(b = 1\times0 + 0\times2=0\)

Step4: Calculate element \(c\)

\(c=0\times3+( - 1)\times0 = 0\)

Step5: Calculate element \(d\)

\(d=0\times0+( - 1)\times2=- 2\)

Answer:

\(a = 3\), \(b = 0\), \(c = 0\), \(d=-2\)