Let L be the linear operator on ℝ n . Suppose that L ( x ) = 0 for some x ≠ 0 . Let A be the matrix representing L with respect to the standard basis { e 1 , e 2 , ... , e n } . Show that A is singular.
Let L be the linear operator on ℝ n . Suppose that L ( x ) = 0 for some x ≠ 0 . Let A be the matrix representing L with respect to the standard basis { e 1 , e 2 , ... , e n } . Show that A is singular.
Solution Summary: The author explains that L is a linear operator on Rn. Let A be the matrix representing L with respect to the standard basis.
Let L be the linear operator on
ℝ
n
. Suppose that
L
(
x
)
=
0
for some
x
≠
0
. Let A be the matrix representing L with respect to the standard basis
{
e
1
,
e
2
,
...
,
e
n
}
. Show that A is singular.
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