2. (a) Define the dot product of two polynomials p(x) = ao+a₁x+a₂x²+a3x³ and q(x) = bo+b₁x+b₂x²+b3x³ from P3(x) as p q = aobo + a₁b₁ + a2b2+ a3b3. Given W = = Span{3x³. - x, 3x² + 2x + 1} a subspace of P3(x), find W¹. (b) For the plane P: -5x + 4y - 3z = 0, compute a basis for each P and P¹.
2. (a) Define the dot product of two polynomials p(x) = ao+a₁x+a₂x²+a3x³ and q(x) = bo+b₁x+b₂x²+b3x³ from P3(x) as p q = aobo + a₁b₁ + a2b2+ a3b3. Given W = = Span{3x³. - x, 3x² + 2x + 1} a subspace of P3(x), find W¹. (b) For the plane P: -5x + 4y - 3z = 0, compute a basis for each P and P¹.
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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