1 A Hilbert matrix is a square matrix created by the following algorithm: 1 Hij %3D i+j-1 Use a nested for loop to create a 6 x 6 Hilbert matrix. You'll need to first create a 6 x 6 matrix full of zeros, then use a nested loop and the formula above to calculate each entry of this matrix. An example of nested loop can be found in Mar 9 notes. Is this matrix "hard" to invert? How do you know? Hint: Try computing by hand the first row of this matrix. Recognize what remains unchanged and what changes in each entry. The unchanged will be the outer loop.

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