Exercise 1.4

Question

Let $f_1,\ldots,f_8$ be a set of functions defined on the interval $[1, 8]$ with
the property that for any numbers $d_1, \ldots, d_8$, there exists a set of coefficients
$c_1,\ldots,c_8$ such that
$$\sum_{j=1}^{8}c_j f_j(i) = d_i, \quad i=1,\ldots,8.$$
(a) Show by appealing to the theorems of this lecture that $d_1, \ldots, d_8$ determine $c_1, \ldots,c_8$ uniquely.
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(b) Let $A$ be the $8 	imes 8$ matrix representing the linear mapping from data
$d_1,\ldots,d_8$ to coefficients $c_1,\ldots,c_8$. What is the $i,j$ entry of $A^{-1}$?

Desh Raj · Accepted Answer

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Exercise 1.4

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Exercise 1.4

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