Using 2x2 Matrices for Plane Transformations
Geometry · Flashcards
GEOMETRY · FLASHCARDS
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QUESTION
What is the determinant of
A
=
(
1
0
0
−
1
)
A=\begin{pmatrix}1&0\\0&-1\end{pmatrix}
A
=
(
1
0
0
−
1
)
?
QUESTION
A region has area
12
12
12
. What is its image area under a matrix with
det
(
A
)
=
1
2
\det(A)=\frac{1}{2}
det
(
A
)
=
2
1
?
QUESTION
If
det
(
A
)
=
4
\det(A)=4
det
(
A
)
=
4
, what is the area scale factor of
A
−
1
A^{-1}
A
−
1
?
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ANSWER
1
4
\frac{1}{4}
4
1
. Area scale factor is
∣
1
4
∣
=
1
4
|\frac{1}{4}| = \frac{1}{4}
∣
4
1
∣
=
4
1
.
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