Let R[x] be a linear space with all polynomials p(x) = ax² + bx + c (a, b, c € R) whose degreeis no more than 2. Let L be the operator on R[x]3 defined by42L(ax² + bx + c) = (a + 3b +6c)x² + (-=a 3b4c)x+ ²a +33(1) Find the matrix A representing L with respect to basis [1,2x, 3x²];a + b + c)(2) Find the matrix B representing L with respect to basis [1-2x+3x2²,-1+2x, −1+3x²];(3) Is the matrix A diagonalizable? Why?

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Let R[x] be a linear space with all polynomials p(x) = ax²+bx+c (a, b, c E R) whose degree is no more than 2. Let L be the operator on R[x], defined by 4 2 L(ax² + bx + c) = (a + 3b +6c)x² + (-=a −: 3b-4c)x+(a+b+c) -Ga 3 3 (1) Find the matrix A representing L with respect to basis [1,2x, 3x²]; (2) Find the matrix B representing L with respect to basis [1-2x+3x², -1 + 2x, -1+3x²]; (3) Is the matrix A diagonalizable? Why?

Let R[x] be a linear space with all polynomials p(x) = ax²+bx+c (a, b, c E R) whose degree is no more than 2. Let L be the operator on R[x], defined by 4 2 L(ax² + bx + c) = (a + 3b +6c)x² + (-=a −: 3b-4c)x+(a+b+c) -Ga 3 3 (1) Find the matrix A representing L with respect to basis [1,2x, 3x²]; (2) Find the matrix B representing L with respect to basis [1-2x+3x², -1 + 2x, -1+3x²]; (3) Is the matrix A diagonalizable? Why?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 56E

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