Vfrdtyky

I am trying to plot the first row of my matrix against time t but I cannot figure out why my matrix yields the error: "vertcat:
Dimensions of matrices being concatenated are not consistent."

t = linspace(0,100);



y_mat = (1./t).*([1, t+(1/2)*exp(-3*t)-(1/2)*exp(-t); 

(3/2)*(exp(-t)-exp(-3*t)), 1-(3/2)*exp(-3*t)+ 

(1/2)*exp(-t)] * [(t-4)/3;1]);



plot(t,y_mat(1,:))

You can also write it out more explicitly. The equation reads:

[ 1,pt2 ; pt3,pt4 ] * [ pt5 ; 1 ] = [ pt5 + pt2 ; pt3.*pt5 + pt4 ]

Since each of those terms is a scalar, you can compute them for all t at the same time using element-wise multiplication:

t = linspace(0,100);



pt2 = t+(1/2)*exp(-3*t)-(1/2)*exp(-t);

pt3 = (3/2)*(exp(-t)-exp(-3*t));

pt4 = 1-(3/2)*exp(-3*t)+(1/2)*exp(-t);



pt5 = (t-4)/3;



y_mat = (1./t) .* [ pt5 + pt2 ; pt3.*pt5 + pt4 ];



plot(t,y_mat)

This might be a bit more verbose, but I don't think it's any less readable than other solutions. And it is much more efficient: 0.0571 ms, versus 483.3 ms (syms solution) and 0.681 ms (loop solution), for a t with 500 elements.

(Note that multiplying by 1./t uses implicit singleton expansion. This works in MATLAB R2016b and newer. For older versions of MATLAB, use bsxfun.)

You are thinking in the term of symbolic notation but implementing in matrix notation. When you do t = linspace(0,100); it creates a 1x100 matrix (array). So when later on it is used in the definition of y_mat, each expression used in the definition evaluates to 1x100 matrix. So your y_mat definition is tying to do this : [1x100] * [1 1x100 ; 1x100 1x100] * [1x100 ; 1] which obviously fails.

You have two options:
Do all computations in the matrix notation by first computing the matrix multiplication separately and restructuring the matrices to represent the actual multiplication (ensure the 1s are appropriately replicated).

OR

use Matlabs's symbolic variables and expressions probably like this :

syms t  % creating symbolic variable

% creating symbolic expressions

f0 = 1/t  

f1 = t+(1/2)*exp(-3*t)-(1/2)*exp(-t);

f2 = (3/2)*(exp(-t)-exp(-3*t));

f3 = 1-(3/2)*exp(-3*t)+(1/2)*exp(-t);

f4 = (t-4)/3;

% defining y_mat

y_mat = f0 * [1 f1; f2 f3] * [f4 ; 1]



% putting value in symbolic variable

t = linspace(eps,100); % eps to avoid division by 0 error



% substitute values and evaluate y_mat

y_mat_vals = eval(subs(y_mat));

This gives y_mat_vals a 2x100 matrix, as the answer.

YOu have messed up your code..you need to be careful when typing such functions. To make it simple, I have used a loop.

t = linspace(0,100);



nt = length(t) ;

y_mat = zeros(2,nt) ;



for i = 1:nt

y_mat(:,i) = (1/t(i))*([1           t(i)+(1/2)*exp(-3*t(i))-(1/2)*exp(-t(i));

    (3/2)*(exp(-t(i))-exp(-3*t(i)))   1-(3/2)*exp(-3*t(i))+(1/2)*exp(-t(i))])*[(t(i)-4)/3;1];

end

plot(t,y_mat)