Determine the type of transformation represented by the following matrix.

Reflection with respect to the Select

Ask by Floyd Bryant. in the United States

Mar 20,2025

Question

Determine the type of transformation represented by the following matrix. $$ \left[\begin{array}{cc}1 & 0 \ 0 & -1\end{array}ight] $$ Reflection with respect to the Select

UpStudy AI · Accepted Answer

1. The given matrix is 
   $$
   A = \begin{pmatrix} 1 & 0 \ 0 & -1 \end{pmatrix}.
   $$
   
2. Notice that when this matrix acts on a vector 
   $$
   \begin{pmatrix} x \ y \end{pmatrix},
   $$
   the result is 
   $$
   A \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \cdot x + 0 \cdot y \ 0 \cdot x + (-1) \cdot y \end{pmatrix} = \begin{pmatrix} x \ -y \end{pmatrix}.
   $$
   
3. This operation leaves the $$x$$-coordinate unchanged while reversing the $$y$$-coordinate. Such a transformation reflects every point across the $$x$$-axis.

4. Therefore, the matrix $$ A $$ represents a reflection with respect to the $$x$$-axis.
The matrix represents a reflection across the x-axis.

Determine the type of transformation represented by the following matrix.

Reflection with respect to the Select

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Determine the type of transformation represented by the following matrix. Reflection with respect to the Select