Solving Systems Using Matrix Inverses
Algebra · Flashcards · Application
ALGEBRA · FLASHCARDS
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QUESTION
Identify the correct criterion:
A
A
A
is invertible iff
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
or
det
(
A
)
≠
0
\det(A)\neq 0
det
(
A
)
=
0
?
QUESTION
Identify whether
A
=
(
1
2
2
4
)
A=\begin{pmatrix}1&2\\2&4\end{pmatrix}
A
=
(
1
2
2
4
)
is invertible.
QUESTION
What is
A
−
1
A^{-1}
A
−
1
for
A
=
(
2
0
0
5
)
A=\begin{pmatrix}2&0\\0&5\end{pmatrix}
A
=
(
2
0
0
5
)
?
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ANSWER
A
−
1
=
(
1
2
0
0
1
5
)
A^{-1}=\begin{pmatrix}\frac{1}{2}&0\\0&\frac{1}{5}\end{pmatrix}
A
−
1
=
(
2
1
0
0
5
1
)
. The inverse of a diagonal matrix reciprocates each diagonal entry.
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