Matrix Transformations of Vectors
Precalculus · Flashcards
PRECALCULUS · FLASHCARDS
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QUESTION
What is
A
(
1
1
)
A\begin{pmatrix}1\\1\end{pmatrix}
A
(
1
1
)
if
A
=
(
2
−
1
4
3
)
A=\begin{pmatrix}2&-1\\4&3\end{pmatrix}
A
=
(
2
4
−
1
3
)
?
QUESTION
What is the output type of multiplying a matrix
A
A
A
by a column vector
v
⃗
\vec{v}
v
(with compatible dimensions)?
QUESTION
What is the result of applying
A
A
A
then
B
B
B
to a vector
v
⃗
\vec{v}
v
, written as one matrix times
v
⃗
\vec{v}
v
?
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ANSWER
B
(
A
v
⃗
)
=
(
B
A
)
v
⃗
B(A\vec{v})=(BA)\vec{v}
B
(
A
v
)
=
(
B
A
)
v
. Composition of transformations equals product of matrices.
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