Consider the polynomials p₁ (t) = 2 + t, p₂ (t) = 2 -t, and p3(t) = 4 (for all t). By inspection, write a linear dependence relation among P₁, P2, and p3. Then find a basis for Span (P₁, P2, P3}. Find a linear dependence relation among P₁, P2, and P3 = + P₁ (Simplify your answers.) P2 Find a basis for Span (P₁, P2, P3}. Choose the correct answer below. A. {P₁, P2, P3} B. {P₁, P₂} C. {+1, 2+2t} D. {P₁ + P₂, P3} P3. O E. {P₁} OF. {P3}
Consider the polynomials p₁ (t) = 2 + t, p₂ (t) = 2 -t, and p3(t) = 4 (for all t). By inspection, write a linear dependence relation among P₁, P2, and p3. Then find a basis for Span (P₁, P2, P3}. Find a linear dependence relation among P₁, P2, and P3 = + P₁ (Simplify your answers.) P2 Find a basis for Span (P₁, P2, P3}. Choose the correct answer below. A. {P₁, P2, P3} B. {P₁, P₂} C. {+1, 2+2t} D. {P₁ + P₂, P3} P3. O E. {P₁} OF. {P3}
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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Transcribed Image Text:Consider the polynomials p₁ (t) = 2 + t, p₂ (t) = 2 -t, and p3(t) = 4 (for all t). By inspection, write a
linear dependence relation among P₁, P2, and p3. Then find a basis for Span (P₁, P2, P3}.
Find a linear dependence relation among P₁, P2,
and
P3 =
P₁ +
(Simplify your answers.)
P2
Find a basis for Span (P₁, P2, P3}. Choose the correct answer below.
A. {P₁, P2, P3}
B. {P₁, P₂}
C. {+1, 2+2t}
D. {P₁ + P₂, P3}
P3.
O E. {P₁}
OF. {P3}
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