Solving Matrices with Symbolic Variables

I am trying to figure out how to solve a problem such as [A]{X}={0} where [A] is a numerical matrix such as

[1 2 3 4]
[5 6 7 8]
[9 0 1 2]

and {X} is a symbolic matrix with a single numeric value such as

[1x1 sym; 1x1 sym; 1x1 sym; 1] 
that is:

[a]
[b]
[c]
[1]

Is there a way to find a,b,c such that [A]{X}={0}

[Shivam Prajapati]

null(A)

[Walter Roberson]

null() by itself does not work for the case where one or more of the X vectors are known constants, as is required by the Question.

Answer 1

[Andrei Bobrov]

A =[ 1     2     3     4
     5     6     7     8
     9     0     1     2]
syms a b c
x = [a;b;c]
k = A(:,1:3)\-A(:,end);
for i1 = 1 : numel(x)
    eval([char(x(i1)),'=k(i1)']);
end

[Jared]

thanks alot works well, one minor adjustment:

k = cell2mat(A(:,1:3))\-cell2mat(A(:,end));

[Karan Gill]

It's much simpler. See Kaixiang Wang's answer below.

[JITHA K R]

Can you explain the working of this code pls?

Answer 2

[Kaixiang Wang]

Simply use MATLAB symbolic toolbox and the solve() function.

syms a b c
A=[1 2 3 4;5 6 7 8;9 0 1 2]
X=[a;b;c;1]
sol=solve(A*X)

[Shivam Prajapati]

Null(A) % null is matlab command

[Walter Roberson]

null() by itself does not work for the case where one or more of the X vectors are known constants, as is required by the Question.

Answer 3

[Walter Roberson]

Linear algebra with symbolic matrices is discussed at http://www.mathworks.com/products/symbolic/

[Charles]

how to downvote this answer?

[Walter Roberson]

In particular these days, that page leads to https://www.mathworks.com/help/symbolic/linear-algebra.html

[Dyuman Joshi]

@Charles, Why exactly do you want to that?