Question

find the given elements of matrix d:
d=left\begin{array}{ccc}-2& - 4&2\\0&6&4end{array}
ight-left\begin{array}{ccc}-2&-2&-2\\4&4&4end{array}
ight
(d_{11}=\boxed{0}checkmark d_{12}=\boxed{-2}checkmark d_{13}=\boxed{4}checkmark)
(d_{21}=\boxed{-4}checkmark d_{22}=\boxed{2}checkmark d_{23}=\boxed{0}checkmark)
complete
this subtraction represents a translation of the given triangle 2 units right (checkmark) and 4 units down (checkmark).
retry

Explanation:

Step1: Subtract corresponding elements

For \(d_{11}\): \((- 2)-(-2)=0\)
For \(d_{12}\): \((-4)-(-2)=-2\)
For \(d_{13}\): \(2 - (-2)=4\)
For \(d_{21}\): \(0 - 4=-4\)
For \(d_{22}\): \(6 - 4 = 2\)
For \(d_{23}\): \(4 - 4=0\)

Step2: Analyze translation

If we consider a point \((x,y)\) in the original triangle and the transformation matrix operation. The general form of a 2 - D translation matrix for a point \((x,y)\) is \(

$$\begin{bmatrix}x\\y\end{bmatrix}$$

+

$$\begin{bmatrix}a\\b\end{bmatrix}$$

\). Here, if we consider the matrix subtraction results as translation values for each vertex of the triangle. The \(x\) - component of the translation is positive (indicating right - ward movement) and \(y\) - component is negative (indicating downward movement). The \(x\) - value change for each vertex is \(2\) (right) and \(y\) - value change is \(-4\) (down).

Answer:

\(d_{11}=0\), \(d_{12}=-2\), \(d_{13}=4\), \(d_{21}=-4\), \(d_{22}=2\), \(d_{23}=0\), translation: 2 units right and 4 units down