Using 2x2 Matrices for Plane Transformations
Precalculus · Flashcards
PRECALCULUS · FLASHCARDS
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QUESTION
What is
det
(
(
cos
θ
−
sin
θ
s
i
n
θ
cos
θ
)
)
\det\!\left(\begin{pmatrix}\cos\theta&-\sin\theta\\sin\theta&\cos\theta\end{pmatrix}\right)
det
(
(
cos
θ
s
in
θ
−
sin
θ
cos
θ
)
)
?
QUESTION
What is the matrix for a dilation by factor
k
k
k
about the origin?
QUESTION
For
A
=
(
0
−
1
1
0
)
A=\begin{pmatrix}0&-1\\1&0\end{pmatrix}
A
=
(
0
1
−
1
0
)
, what is the image of
(
x
,
y
)
(x,y)
(
x
,
y
)
?
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ANSWER
(
−
y
,
x
)
(-y,\,x)
(
−
y
,
x
)
. This matrix rotates by
90
°
90°
90°
counterclockwise.
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