Use mathematical induction to prove that if L is a linear transformation from V to W , then L ( α 1 v 1 + α 2 v 2 + ... + α n v n ) = α 1 L ( v 1 ) + α 2 L ( v 2 ) + ... + α n L ( v n )
Use mathematical induction to prove that if L is a linear transformation from V to W , then L ( α 1 v 1 + α 2 v 2 + ... + α n v n ) = α 1 L ( v 1 ) + α 2 L ( v 2 ) + ... + α n L ( v n )
Solution Summary: The author explains that L is a linear transformation from V to W.
Use mathematical induction to prove that if L is a linear transformation from V to W, then
L
(
α
1
v
1
+
α
2
v
2
+
...
+
α
n
v
n
)
=
α
1
L
(
v
1
)
+
α
2
L
(
v
2
)
+
...
+
α
n
L
(
v
n
)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
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