If is a real matrix, there is a geometrical interpretation of det ( Let 11 and 22 be points in the plane, forming a triangle with the origin 1. Let 1112 be the polar coordinate representation of...

If

is a real matrix, there is a geometrical interpretation of det

(
Let

<sub>1

1</sub>

and

<sub>2

2</sub>

be points in the plane, forming a triangle with the origin

1. Let

<sub>1

1

1

2</sub>

be the polar coordinate representation of

<sub>1

1

2</sub>, y₂

and

<sub>2

1</sub>

Show that apart from sign, is the area of the triangle

2. Find the area of a parallelogram as a determinant.