Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b + 2c)x + (b + 2c)x2 1) Is T cyclic? 2) Is T irreducible? 3) Is T indecomposable?
Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b + 2c)x + (b + 2c)x2 1) Is T cyclic? 2) Is T irreducible? 3) Is T indecomposable?
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 4CM
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Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b + 2c)x + (b + 2c)x2
1) Is T cyclic?
2) Is T irreducible?
3) Is T indecomposable?
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