Let T P3 P3 be the linear transformation such that T(2x²) = 2x² - 4x, T(0.5x + 3) = 3x² + 2x - 2, T(2x² + 1) = −2x − 3. Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²)=x²-2x ✓ T(ax² + bx + c) = = Let be the plane with equation X1 ― - 3x2 - 2x3 = 0 in R³. The linear transformation T (B) - E 1 7 -107 x1 1 -2 x2 2 2 -2 x3 maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis A = = [88

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
Question
Let T P3 P3 be the linear transformation such that
T(2x²) = 2x² - 4x, T(0.5x + 3) = 3x² + 2x - 2, T(2x² + 1) = −2x − 3.
Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers.
T(1) =
T(x) =
T(x²)=x²-2x ✓
T(ax² + bx + c) =
=
Transcribed Image Text:Let T P3 P3 be the linear transformation such that T(2x²) = 2x² - 4x, T(0.5x + 3) = 3x² + 2x - 2, T(2x² + 1) = −2x − 3. Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²)=x²-2x ✓ T(ax² + bx + c) = =
Let be the plane with equation X1
―
- 3x2 - 2x3 = 0 in R³. The linear transformation
T
(B) - E
1 7
-107
x1
1 -2 x2
2 2 -2
x3
maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V.
Find the matrix A of the restricted map Ĩ: V → V with respect to the basis
A =
=
[88
Transcribed Image Text:Let be the plane with equation X1 ― - 3x2 - 2x3 = 0 in R³. The linear transformation T (B) - E 1 7 -107 x1 1 -2 x2 2 2 -2 x3 maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis A = = [88
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