(a) Consider the ordered basis ß = [1,1 + x, 1 + x + x²] for V = P₂ and F = R. Suppose is in P2 and you know these coordinates: [7], = (1, 2, 3). Find the vector V.
(a) Consider the ordered basis ß = [1,1 + x, 1 + x + x²] for V = P₂ and F = R. Suppose is in P2 and you know these coordinates: [7], = (1, 2, 3). Find the vector V.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![7.
(a) Consider the ordered basis ß = [1,1 +x, 1 + x + x²] for V = P₂ and F = R.
Suppose is in P2 and you know these coordinates: [] = (1, 2, 3).
Find the vector 7.
(b) Let A be a 2 x 2 matrix and a be a real number. Prove that
det (a A)=a² det(A)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0dbe0800-3ed1-4c93-80b7-6ba53d418546%2Ffbc5a473-9cb2-4142-844e-8f9105aa7b3f%2Furrmfy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.
(a) Consider the ordered basis ß = [1,1 +x, 1 + x + x²] for V = P₂ and F = R.
Suppose is in P2 and you know these coordinates: [] = (1, 2, 3).
Find the vector 7.
(b) Let A be a 2 x 2 matrix and a be a real number. Prove that
det (a A)=a² det(A)
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