solve linear equation system based on matrix ("Matrix dimension must agree")

Question

I have a given matrix of size NxN (called M),a vector of Nx1 (called V), and two scalars (called a and b). I want to solve the linear system of equations for alpha. The dimensions are given as MATLAB reports them using the function size(-).

(M + a * b * 1) alpha == V

with 1 being a matrix of just 1s.

I figured the easiest way to do so would be

syms alpher; 
Mprep = (M + a * b * ones(length(M),length(M))); 
eqn = Mprep * alpher == V;
alpha = solve(eqn,alpher)

However, I get the error

Error using ==
Matrix dimensions must agree

I am not sure whether this error is due to the fact that Matlab does not know the proper size of alpher or if I am just plain wrong in my approach. The error occurs in the second last line according to matlab.

What is the best way to solve this in MATLAB?

as in this case M = N based on M being symmetric and thus ones(length(M),length(M)) having the same dimensions as M itself. Additionally the error occurs in the second last line so any presumed error in a previous line is rather unlikely. (this was a response to a now deleted comment) — Sim

Suever Suever · Accepted Answer · 2017-01-19T14:03:33

If you want to solve for an array of symbolic variables, you actually have to create an array of symbolic variables. Currently MATLAB sees alpher as a scalar and this obviously has dimension issues when performing matrix multiplication since an N x N matrix times a scalar is not equal to an N x 1 array.

Rather than using the symbolic toolbox at all, I would recommend simply using MATLAB's built-in ability to solve a linear system of equations using the \ operator (mldivide)

alpha = Mprep \ V;

As a side note, please refrain from using length as the result is ambiguous as it simply returns the first non-singleton dimension. If you want the size of the ones to be equal to M just use ones(size(M)), alternately if you specifically want the number of rows or columns in M use the second input to size to specify the dimension that you'd like to query: nRows = size(M, 1) or nCols = size(M, 2)

solve linear equation system based on matrix ("Matrix dimension must agree")

1 Answers