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

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

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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