Let A be a 2 × 2 matrix, and let L A be the linear operator defined by L A ( x ) = A x Show that (a) L A maps ℝ 2 onto the column space of A . (b) if A is nonsingular, then L A maps ℝ 2 onto ℝ 2
Let A be a 2 × 2 matrix, and let L A be the linear operator defined by L A ( x ) = A x Show that (a) L A maps ℝ 2 onto the column space of A . (b) if A is nonsingular, then L A maps ℝ 2 onto ℝ 2
Solution Summary: The author illustrates how L_A maps to the column space of A — let A be a 2times 2 matrix.
Let A be a
2
×
2
matrix, and let
L
A
be the linear operator defined by
L
A
(
x
)
=
A
x
Show that (a)
L
A
maps
ℝ
2
onto the column space of A. (b) if A is nonsingular, then
L
A
maps
ℝ
2
onto
ℝ
2
Intermediate Algebra for College Students (7th Edition)
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