Let x1, x2, and x3 be distinct real numbers such that x1 (a) Show that T is
Question:
(a) Show that T is a linear transformation.
(b) Show that T is one-to-one.
(c) Verify that if a1, a2, and a3 are any real numbers, then
Where
(d) What relationship exists between the graphs of the function
a1P1(x) + a2P2(x) + a3P3(x)
and the points (x1, a1), (x2, a2), and (x3, a3)?
Transcribed Image Text:
p(xi) T(p(x)) = | p(x2) p(x3) αι a3 (x-x2) (x-x2) P3(x) =-(a-na-w P3(x) = P (x)= (x2-x1)(x2-r ) 2-*1)(x2-x3 3-X1) (X3-X2)
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a We have and b Since T is defined for quadratic polynomials only and the numbers x 1 x ...View the full answer
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
Question Posted:
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