# Solving system of equations

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Hi expert,

May I ask your suggestion on how to solve the following matrix system,

where the component of the matrix A is complex numbers with the angle (theta) runs from 0 to 2*pi, and n = 9. The known value z = x + iy = re^ia, is also complex numbers as such, r = sqrt(x^2+y^2) and a = atan (y/x)

Suppose matrix z is as shown below,

z =

0 1.0148

0.1736 0.9848

0.3420 0.9397

0.5047 0.8742

0.6748 0.8042

0.8419 0.7065

0.9919 0.5727

1.1049 0.4022

1.1757 0.2073

1.1999 0

1.1757 -0.2073

1.1049 -0.4022

0.9919 -0.5727

0.8419 -0.7065

0.6748 -0.8042

0.5047 -0.8742

0.3420 -0.9397

0.1736 -0.9848

0 -1.0148

How do you solve the system of equations above i.e. to find the coefficient of matrix alpha. I tried using a simple matrix manipulation X = inv((tran(A)*A))*tran(A)*z, but I cannot get a reasonable result.

I would expect the solution i.e. components of matrix alpa to be a real numbers.

##### 0 Comments

### Accepted Answer

Matt J
on 1 Jan 2018

Edited: Matt J
on 1 Jan 2018

What do the two columns of z mean? Is the 2nd column supposed to be the imaginary part of z? If so,

Z=complex(z(:,1),z(:,2));

X = A\Z

##### 11 Comments

Matt J
on 17 Feb 2018

If the first value is 1, then this just leads to a mild modification of my initial proposal,

zc=complex(z(:,1),z(:,2));

alpha=A(:,2:end)\(zc-A(:,1))

This solves for the unknown alpha (alpha2,...,alphaN).

Jan
on 25 Apr 2019

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