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# Gaussian elimination

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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.

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