X1 xí V = 1 X2 X3 det V = (x2 – x1)(x3 – x)(x3 – x2) Let x1, x2 and x3 be fixed numbers all distinct. Matrix V can be used to find an interpolating quadratic polynomial for the points (x1, yı), (x2, y2) and (x3, y3), where y1 , y2 and y3 are arbitrary prove the existence of an interpolating polyno- mial p(t) = co +c¡t + c2t² such that p(x1) = y1, p(x2) = У, and p(x;) — Уз .
X1 xí V = 1 X2 X3 det V = (x2 – x1)(x3 – x)(x3 – x2) Let x1, x2 and x3 be fixed numbers all distinct. Matrix V can be used to find an interpolating quadratic polynomial for the points (x1, yı), (x2, y2) and (x3, y3), where y1 , y2 and y3 are arbitrary prove the existence of an interpolating polyno- mial p(t) = co +c¡t + c2t² such that p(x1) = y1, p(x2) = У, and p(x;) — Уз .
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 47E
Related questions
Question
Transcribed Image Text:1
X1
V
1
X2
X3
det V =
(x2 – x1)(x3 – X)(x3 – x2)
Let x1, x2 and x3 be fixed numbers all distinct. Matrix V can
be used to find an interpolating quadratic polynomial for the
points (x1, yı), (x2, y2) and (x3, y3), where y , y2 and y3 are
arbitrary
prove the existence of an interpolating polyno-
mial p(t) = co +c;t + c2t² such that p(x1) = y1, p(x2) =
V2 and p(x3) = y3 ·
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage