# Gaussian elimination

1. Solve the following system of equations by hand. Use the Gaussian elimination, on the augmented matrix, and write the row operation you used next to each new row.

x + y + z = 0

3x - 2y + 2z = -14

2x + 3y - z = 22

2. Find all roots of the equation z^5 = i, i.e. find the five values of i^(1/5) and show them on an Argand diagram.

3. A cylindrical petrol storage tank is to be constructed of metal on a concrete base. Find the relation between the radius of the base and the height of a tank so that the amount of metal used is the least possible to hold a given volume V0.

4. Find the area enclosed between the curve y = x (x-1)^2 and the axis y=0, establishing first where they intersect.

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#### Solution Summary

Gaussian elimination is established. The expert finds all the roots of the equation.