# Problem 7.14. Let (æ1,...,am+1) be a sequence of pairwise distinct scalars in R and let(B1,...,Bm+1) be any sequence of scalars in R, not necessarily distinct.(1) Prove that there is a unique polynomial P of degree at most m such thatP(a4) Bi, 1i

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Hello, kindly assist me with the solution to Q4. I will appreciate it if you provide a very detailed solution, thanks help_outlineImage TranscriptioncloseProblem 7.14. Let (æ1,...,am+1) be a sequence of pairwise distinct scalars in R and let (B1,...,Bm+1) be any sequence of scalars in R, not necessarily distinct. (1) Prove that there is a unique polynomial P of degree at most m such that P(a4) Bi, 1i
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Step 1

Basis and Dual basis are given as, help_outlineImage Transcriptioncloseand (4.5. (4.L. 0 if i j .1) if i= j m+1 So, LL 1 if i = j [0 if i Since, L, ()1 if i = j fullscreen
Step 2

Hence, equation (1) can also be written as

Step 3

Above equation can also be writt...

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