Solving Systems Using Matrix Inverses
Algebra 2 · Flashcards
ALGEBRA 2 · FLASHCARDS
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QUESTION
What is the relationship between
det
(
A
)
\det(A)
det
(
A
)
and the number of solutions to
A
x
⃗
=
b
⃗
A\vec{x}=\vec{b}
A
x
=
b
?
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
)
?
QUESTION
What is the identity matrix
I
3
I_3
I
3
?
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ANSWER
I
3
=
(
1
0
0
0
1
0
0
0
1
)
I_3=\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}
I
3
=
1
0
0
0
1
0
0
0
1
. The 3x3 identity matrix has 1s on the main diagonal and 0s elsewhere, acting as the multiplicative identity.
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