Linear Algebra and Its Applications · Problem 7.2.21

Computations with Matrices — Gilbert Strang

Mathematics · hilbert-matrix-condition-number

Problem

Compute the exact inverse of the Hilbert matrix

A

by elimination. Then compute

A^{-1}

again by rounding all numbers to three figures:

\text{In MATLAB}: \quad A = \text{hilb}(3) = \begin{bmatrix} 1 & \frac{1}{2} & \frac{1}{3} \\ \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \end{bmatrix}.