Write as a Vector Equality

Problem

{[1=(a_0)+(a_1)(1)+(a_2)*(1)2],[2=(a_0)+(a_1)(2)+(a_2)*(2)2],[3=(a_0)+(a_1)(3)+(a_2)*(3)2])

Solution

1. Identify the components of the system of linear equations where the variables are (a_0) (a_1) and (a_2)

2. Rewrite each equation by evaluating the powers of the inputs 1 2 and 3

3. Construct the vector on the left side using the constants 1 2 and 3

4. Express the right side as a product of a coefficient matrix (the Vandermonde matrix) and the vector of unknowns a

Final Answer

[[1],[2],[3]]=[[1,1,1],[1,2,4],[1,3,9]]*[[(a_0)],[(a_1)],[(a_2)]]

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