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For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). 1) Let T a = la + 1b+2c la + 3b +6c i) A basis for Range(T) would be: la + 2b + 4c] la + 2b +4c] ii) The Range of this transformation spans the entire codomain:

For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). 1) Let T a = la + 1b+2c la + 3b +6c i) A basis for Range(T) would be: la + 2b + 4c] la + 2b +4c] ii) The Range of this transformation spans the entire codomain:

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...
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For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). a 13-1 = 1) Let T b la + 1b+2c la + 3b +6c i) A basis for Range(T) would be: ii) The Range of this transformation spans the entire codomain: 2) Let T(a + bx + cx² + dx³) = 1a + 2b + 4c 1a + 2b + 4c] i) A basis for Range(T) would be: la + (-1) b + 1c + 1d 6a+ (-4) b + 8c+5d ii) The Range of this transformation spans the entire codomain: 2a+ (-1) b + 3c + 1d 9a +(-5) b + 13c + 6d]
Transcribed Image Text:For each linear transformation below, state a basis for Range(T) and then indicate if the Range spans the entire codomain.. If you do not need a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the first two vectors and make all subsequent vectors have 0 for all boxes). a 13-1 = 1) Let T b la + 1b+2c la + 3b +6c i) A basis for Range(T) would be: ii) The Range of this transformation spans the entire codomain: 2) Let T(a + bx + cx² + dx³) = 1a + 2b + 4c 1a + 2b + 4c] i) A basis for Range(T) would be: la + (-1) b + 1c + 1d 6a+ (-4) b + 8c+5d ii) The Range of this transformation spans the entire codomain: 2a+ (-1) b + 3c + 1d 9a +(-5) b + 13c + 6d]
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