Zero and Identity Matrices and Determinants
Geometry · Flashcards
GEOMETRY · FLASHCARDS
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QUESTION
What is
A
+
I
n
A+I_n
A
+
I
n
called when
A
A
A
is
n
×
n
n\times n
n
×
n
?
QUESTION
If
det
(
A
)
=
1
4
\det(A)=\frac{1}{4}
det
(
A
)
=
4
1
, what is
det
(
A
−
1
)
\det(A^{-1})
det
(
A
−
1
)
?
QUESTION
If
det
(
A
)
≠
0
\det(A)\ne 0
det
(
A
)
=
0
, what must be true about the equation
A
X
=
I
AX=I
A
X
=
I
?
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ANSWER
It has the unique solution
X
=
A
−
1
X=A^{-1}
X
=
A
−
1
. Nonzero determinant guarantees unique solution exists.
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