Question

triangle abc is translated using matrix subtraction. which represents the resulting s after the translation?
\\( \left \

$$\begin{array} { c c c } { - 3 } & { 4 } & { - 2 } \\ { 4 } & { 3 } & { - 2 } \\end{array}$$

\
ight - \left \

$$\begin{array} { c c c } { 3 } & { 3 } & { 3 } \\ { - 1 } & { - 1 } & { - 1 } \\end{array}$$

\
ight \\)

Explanation:

Step1: Matrix subtraction rule

When subtracting two matrices, we subtract the corresponding elements. For a matrix \(

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

-

$$\begin{bmatrix}g&h&i\\j&k&l\end{bmatrix}$$

=

$$\begin{bmatrix}a - g&b - h&c - i\\d - j&e - k&f - l\end{bmatrix}$$

\)

Step2: Subtract the first - row elements

For the first - row elements:
\(-3-3=-6\), \(4 - 3=1\), \(-2-3=-5\)

Step3: Subtract the second - row elements

For the second - row elements:
\(4-(-1)=4 + 1=5\), \(3-(-1)=3 + 1=4\), \(-2-(-1)=-2 + 1=-1\)

Answer:

\(

$$\begin{bmatrix}-6&1&-5\\5&4&-1\end{bmatrix}$$

\)