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What will be the dimension of the coefficient matrix (comprised of the various summations of the...

What will be the dimension of the coefficient matrix (comprised of the various summations of the data) to determine the polynomial coefficients, if you approximate a 4th order polynomial for a given set of data?

a. 4 X 5

b. 4 X 4

c. 5 X 5

d. 5 X 4

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Answer #1

The dimension of the coefficient matrix of a 4th order polynomial will be 4 x 5. It consist of 4 rows and 5 columns.

A 4th order polynomial consist of x4 term, x3 term, x2 term, x term and a constant term. So totally there will be 5 terms and we need at least 4 equations to solve a 4th order polynomial.

The number of rows in the coefficient matrix will be 4, which refers to the number of equations required to solve. The number of columns in the coefficient matrix will be 5, which refers to the number of terms in the polynomial.

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