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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.CM: Cumulative Review

Problem 15CM

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Let T₁: P₂ → R2 and T2 R2 R2x2 be linear transformations defined as follows.
a1
T₁ (αo + α₁ x + a₂2²) = [a² + a₁]
T₂
(T₂0 T₁) (3 + 2x + 5x²) =
Check
3x1
-6x1
-3x2 -9x2.
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Let T be a linear transformation from R³ into R³. Find T-1 T(x1x₂x3) = (2x1-X3, X₁ + X₂ X3, X2-3X3) T(X₁₁X₁₁X3) = (2x₁+x₂ −X3, −3x₁+6x₂−x3, −X₁+2×₂-2x3) b. T(x1x2x3) = (2x₁ + x₂ -2X3, X₂-X3, X1 + X3) c. T(x₁,x₂₁x3) = (2x₁ + x₂ -2X3, X₂-X3, -X₁ + X3) d. T(x1,x2x3) = (4x₁-2×₂-X3, X₁-X₂, −3x₁+2x₂ + x3) T(X₁, X₂2₁×3) = (-x₁ + 3x₂ + 3x3, −3x₁-x₂ + 4x3,2x₁ − ×2 −X3) a. e.
Let T be a linear transformation from P₂ into P₂ such that T(1) = x, T(x) = 1 + x, and 7(x2) = 1 + x + x². Find 7(1 - 7x + 2x²). T(1 - 7x + 2x²) = Need Help? Read It Need Help? Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function. (Use C for the constant of integration.) Dx(f) = 8x + 6 Watch It Read It
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all of part (a) please

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