Let T: P3 Pa be the linear transformation defined by T(at3 + bt2 + ct + d) = (a - b)t3+ (c- d)t. Then, justify your answers: %3D (i) Is T invertible? (ii) Is t3 – t2 +t- 1 in ker T ? (iii) Is 3t3 + t in range T ? (iv) Find a basis of ker T. (v) Find a basis of range T. 4.
Let T: P3 Pa be the linear transformation defined by T(at3 + bt2 + ct + d) = (a - b)t3+ (c- d)t. Then, justify your answers: %3D (i) Is T invertible? (ii) Is t3 – t2 +t- 1 in ker T ? (iii) Is 3t3 + t in range T ? (iv) Find a basis of ker T. (v) Find a basis of range T. 4.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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