Let L: R2x2 → P, be a lincar transformation defined as follos: = (a – b)x² + (b – - - )z + (a – d) 1. Find the matrix representation of L with respect to the standard bsis (E1,E12, E21, Ezz), and the standard basis of P, (x²,x,1). 2. Use (1.) to compute L 3. Find a basis for Ker(L). 4. Find all matrices A E Rx2 such that L(A) = 3x² + 2x + 1, if any. %3D
Let L: R2x2 → P, be a lincar transformation defined as follos: = (a – b)x² + (b – - - )z + (a – d) 1. Find the matrix representation of L with respect to the standard bsis (E1,E12, E21, Ezz), and the standard basis of P, (x²,x,1). 2. Use (1.) to compute L 3. Find a basis for Ker(L). 4. Find all matrices A E Rx2 such that L(A) = 3x² + 2x + 1, if any. %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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الوقت المتبقی 1:28:140
Let L: R2x2 → P, be a linear transformation defincd as follows:
= (a – b)x² + (b – - - )x + (a – d)
1. Find the matrix representation of L with respect to the standard bsis
{E11, E12, E21, Ezz), and the standard basis of P3, {x²,x, 1).
2. Use (1.) to compute L
3. Find a basis for Ker(L).
4. Find all matrices A E R2x2 such that L(A) = 3x² + 2x + 1, if any.
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