**A singuler Set**

The following underdetermined equation set was analyzed in Example 6.4-2. There it was shown that an infinite number of solutions exists. Use the pinv and the rref commands to obtain solutions.

2x-4y+5z=-4

-4x – 2} + 3z = 4

2x + 6)’ – 8;: == 0

**• Solution**

First use the p i nv command. The MATLAB session follows.

»A [2,-4,5;-4,-2,3;2,6,-8];

»b [-4;4;0];

»x pinv(A)*b

x

-1.2148

0.2074

-0.1481

Thus the pseudoinverse method gives the solution: x = -1.2148, )’ = 0.2074, z = -0.1481. This solution is valid, but it is not the general solution.

To obtain the general solution, we can use the rre f command. The current MATLAB session continues as follows.

»rref ([A b])

ans =

x+Oy-0.lz=-1.2

Ox + y – l.3z = 0.4

Ox +Oy -l-Dz = 0

We can easily solve these expressions for x and y in terms of z as follows: x = 0,1z – 1.2 and y = l.3z +0.4. This result is the general solution to the problem, where z is taken to be the arbitrary variable

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