{V1, ..., v {T (v1), . .., T (v,)}, islinearly dependent in W. This fact shows that if a linear transformation : is linearly dependent in V, then the set of images, p3 Show that if maps a onto a linearly independent set {T (V1), ... , T (vp)}, then the original set is set {V] V1,...,' linearly independent, too (because it cannot be linearly dependent).
{V1, ..., v {T (v1), . .., T (v,)}, islinearly dependent in W. This fact shows that if a linear transformation : is linearly dependent in V, then the set of images, p3 Show that if maps a onto a linearly independent set {T (V1), ... , T (vp)}, then the original set is set {V] V1,...,' linearly independent, too (because it cannot be linearly dependent).
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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![{V1, ..., v
{T (v1), . .., T (v,)}, islinearly dependent in W. This fact shows that if a linear transformation :
is linearly dependent in V, then the set of images,
p3
Show that if
maps a
onto a linearly independent set {T (V1), ... , T (vp)}, then the original set is
set
{V]
V1,...,'
linearly independent, too (because it cannot be linearly dependent).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b4ef513-683b-46fb-80c5-755986cdb587%2F7793d67b-403a-43e7-80f8-78d071c1e4fa%2Fbfxuqgd.png&w=3840&q=75)
Transcribed Image Text:{V1, ..., v
{T (v1), . .., T (v,)}, islinearly dependent in W. This fact shows that if a linear transformation :
is linearly dependent in V, then the set of images,
p3
Show that if
maps a
onto a linearly independent set {T (V1), ... , T (vp)}, then the original set is
set
{V]
V1,...,'
linearly independent, too (because it cannot be linearly dependent).
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