We are given that a parallelogram can be represented by the following matrix:
[tex]\begin{bmatrix}{5} & {-5} \\ {2} & {3}\end{bmatrix}[/tex]
The area of a parallelogram represented by a 2x2 matrix is the determinant of the matrix. The determinant of a matrix of the form:
[tex]\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}[/tex]
Is given by:
[tex]det(\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix})=ad-bc[/tex]
Therefore, the determinant is:
[tex]det(\begin{bmatrix}{5} & {-5} \\ {2} & {3}\end{bmatrix})=(5)(3)-(-5)(2)=15+10=25[/tex]
Therefore, the area of the parallelogram is 25 square units.
