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Consider the function T : P.(R) → P,(R) given by T(a + dz + cz²) = (a – b + c) + bz + (-b+2c)r² Find eigenvalues of T and state their algebraic multiplicity.

Consider the function T : P.(R) → P,(R) given by T(a + dz + cz²) = (a – b + c) + bz + (-b+2c)r² Find eigenvalues of T and state their algebraic multiplicity.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 8E
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Would you please go thru the process of finding the values of T

Consider the function T : P,(R) → P,(R) given by T(a + bz + cz³) = (a – 6+c) + bx + (-b+2c)z² Find eigenvalues of T and state their algebraic multiplicity. E Expand Transcribed Image Text Consider the function T:P2|R) - P2 (R) given by T(a+ bx + cx*) = (a - b+ c) + bx+ (-b+2c)x Find eigenvalues of Tand state their algebralc multiplicity. V Expert Answer Step 1 Firstly we will find matrix associated with T. Step 2 T: P, IR)→ P IR) grven by Tla tbx+cx) = (a-b+s)+ bx+ Gb+2c) x? To find eigen valuus of T we finst kind matrin dtouated with wet: standoad. basis of 6 = {1, x,u²}. T(4) = 1 T(x) = -I + x+(-1)x² = - 1+x-x2 T(x²) = 1 +ax? T: B:8) - A= [1 - O -1 Now, for eigen valuus of A we must caluulate JA-AZ1=0. *作。 =0. =) d=1,1, 2. ) del P8 an eigen value with pmalgebraic multipiay2. and d=2 s an elgen value with algebraje mutipuicly
Transcribed Image Text:Consider the function T : P,(R) → P,(R) given by T(a + bz + cz³) = (a – 6+c) + bx + (-b+2c)z² Find eigenvalues of T and state their algebraic multiplicity. E Expand Transcribed Image Text Consider the function T:P2|R) - P2 (R) given by T(a+ bx + cx*) = (a - b+ c) + bx+ (-b+2c)x Find eigenvalues of Tand state their algebralc multiplicity. V Expert Answer Step 1 Firstly we will find matrix associated with T. Step 2 T: P, IR)→ P IR) grven by Tla tbx+cx) = (a-b+s)+ bx+ Gb+2c) x? To find eigen valuus of T we finst kind matrin dtouated with wet: standoad. basis of 6 = {1, x,u²}. T(4) = 1 T(x) = -I + x+(-1)x² = - 1+x-x2 T(x²) = 1 +ax? T: B:8) - A= [1 - O -1 Now, for eigen valuus of A we must caluulate JA-AZ1=0. *作。 =0. =) d=1,1, 2. ) del P8 an eigen value with pmalgebraic multipiay2. and d=2 s an elgen value with algebraje mutipuicly
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