[EX3 Q3 Linear algebra] I have no problem with the rank and nullity, but I can't understand the solution provided for the basis of rank in both (a) and (b), could u please tell me why the provided solution can be the basis? thx :) 3. Find the ranks and nullities of the following linear maps T: U → V, and findbases of the kernel and image of Tin each case.a BB-7(a) U = R³, V = R³, T B(0)(b) U = R², V = R¹, T(2)basis of Ker(T) is()(b) Rank(T)=2, Nullity(T)=0=a possible basis of Im(T) is(a) Rank(T)=2, Nullity(T)=1, a possible basis of Im(T) is-0.0aaa(:¹).and the basis of Ker(T) is empty: 0.and a possible

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Answered: 3. Find the ranks and nullities of the…

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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[EX3 Q3 Linear algebra] I have no problem with the rank and nullity, but I can't understand the solution provided for the basis of rank in both (a) and (b), could u please tell me why the provided solution can be the basis? thx :)

3. Find the ranks and nullities of the following linear maps T: U → V, and find
bases of the kernel and image of Tin each case.
a B
B-7
(a) U = R³, V = R³, T B
(0)
(b) U = R², V = R¹, T
(2)
basis of Ker(T) is
()
(b) Rank(T)=2, Nullity(T)=0
=
a possible basis of Im(T) is
(a) Rank(T)=2, Nullity(T)=1, a possible basis of Im(T) is
-0.0
a
a
a
(:¹).
and the basis of Ker(T) is empty: 0.
and a possible

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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