How to solve implicit (symbolic) equations using MuPad

I am trying to solve a simple system of three equations in MatLab. Trouble is, they are all symbolic.

The three equations are the following:

ez = k

er = i*cos(theta) + j*sin(theta)

et = -i*sin(theta) + j*cos(theta)

I want to solve for i, j and k in Matlab, which will probably require MuPad.

Obviously, the answers are i = er*cos(theta) - et*sin(theta)... etc., but I need to be able to do it in the program as well.

Answer 1

[Walter Roberson]

syms i j k
solve( ez == k, er == i*cos(theta) + j*sin(theta), et = -i*sin(theta) + j*cos(theta), [i, j, k])