5. Let 911 ain a21 azn ⠀ 1 amn am1 am2 be an m x n real matrix. Prove that :R"→ Rm defined as A = 912 a22 is a linear transformation from R" to Rm *** *** A(a) = Aa ER", Va ER"
5. Let 911 ain a21 azn ⠀ 1 amn am1 am2 be an m x n real matrix. Prove that :R"→ Rm defined as A = 912 a22 is a linear transformation from R" to Rm *** *** A(a) = Aa ER", Va ER"
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
M 8
Transcribed Image Text:5. Let
6.
A =
911
912
a21 a22
***
is a linear transformation from R" to Rm.
ain
am1 am2
amn
be an m x n real matrix. Prove that :R"→ Rm defined as
***
azn
A (a) = Aa ER, VER"
Let V₁, V₂ be two subspaces of V, and V₁ C V₂. Show that if V₁ and V₂ have the same
dimension, then V₁ = V₂.
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