A linear transformation L : V → W is said to be map V onto W if L ( V ) = W . Show that the linear transformation L defined by L ( x ) = ( x 1 , x 1 + x 2 , x 1 + x 2 + x 3 ) T maps ℝ 3 onto ℝ 3 .
A linear transformation L : V → W is said to be map V onto W if L ( V ) = W . Show that the linear transformation L defined by L ( x ) = ( x 1 , x 1 + x 2 , x 1 + x 2 + x 3 ) T maps ℝ 3 onto ℝ 3 .
Solution Summary: The author explains that a linear transformation L defined by L(x) is said to map Vonto
A linear transformation
L
:
V
→
W
is said to be map V onto W if
L
(
V
)
=
W
. Show that the linear transformation L defined by
L
(
x
)
=
(
x
1
,
x
1
+
x
2
,
x
1
+
x
2
+
x
3
)
T
maps
ℝ
3
onto
ℝ
3
.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY