MATLAB: Error using * matrix dimensions must agree

errormatrix dimensions

Please note that I have tried using " .* " instead of " * " and it STILL doesn't work. That is the fix that every single similar question has gotten. Afterwards, it just says MATRIX dimensions must agree instead of INNER MATRIX dimensions must agree. Below is my script:
 g = 9.81; t = [15:15:75]; x = [0:5:80]; v = 28; yo = 0;
 y = (tan(t))*x - (g/(2*v^2*(cos(t))^2))*x^2 + yo;
It is supposed to generate results that are assembled in an array where the first dimension (rows) corresponds to the x values, and the second dimension (columns) corresponds to the t values. What should I go about doing in order to fix this error of matrix dimensions?

Best Answer

Your question states that 1st dim should correspond to the x, and the 2nd dim to t. But where are you specifying that? Both x and t are row vectors (and of different lengths), so neither of them specify anything along the 1st dim:
>> size(t)
ans =
     1     5
>> size(x)
ans =
     1    17
Multiply two row vectors of different lengths will be an error, no matter how many different matrix multiply methods you try:
>> tan(t)*x
??? Error using ==> mtimes
Inner matrix dimensions must agree.
>> tan(t).*x
??? Error using ==> times
Matrix dimensions must agree.
There is no standard mathematical definition for multiplying row vectors of different lengths. In this example, what should the 4 multiply with?:
>> [1,2,3,4].*[5,6,7]
??? Error using ==> mtimes
Inner matrix dimensions must agree.
Instead of imagining what the code should be doing, try to pay attention to what the code is really doing. For example, when you read about matrix multiplication then you would realize that you can trivially orient the x as a column, and you get a matrix output when it is multiplied with the row vector t:
 >> x(:)*tan(t)
 ans =
            0            0            0            0            0
        -4.28      -32.027       8.0989       1.6002      -2.1035
      -8.5599      -64.053       16.198       3.2004       -4.207
       -12.84       -96.08       24.297       4.8006      -6.3105
   ... etc
And then this leads directly to one simple solution to your question:
>> g = 9.81;
>> t = 15:15:75;
>> x = 0:5:80;
>> v = 28;
>> yo = 0;
>> y = x(:)*tan(t) - (x(:).^2) * (g./(2*v^2*(cos(t)).^2)) + yo
y =
          0            0            0            0            0
     -4.551        -38.6       7.5321       1.4278      -2.2876
     -9.644      -90.348       13.931       2.5107      -4.9434
    -15.279      -155.24       19.196       3.2487      -7.9673
    -21.456      -233.28       23.327       3.6419      -11.359
    -28.175      -324.47       26.325       3.6903       -15.12
    -35.436      -428.81       28.189       3.3937      -19.248
    -43.239      -546.29        28.92       2.7524      -23.745
    -51.585      -676.92       28.517       1.7661       -28.61
    -60.472       -820.7       26.981        0.435      -33.843
    -69.901      -977.63       24.311       -1.241      -39.444
    -79.872      -1147.7       20.508      -3.2618      -45.414
    -90.386      -1330.9       15.571      -5.6275      -51.751
    -101.44      -1527.3       9.5002       -8.338      -58.457
    -113.04      -1736.8       2.2961      -11.393      -65.531
    -125.18      -1959.5      -6.0416      -14.794      -72.973
    -137.86      -2195.3      -15.513      -18.539      -80.784
Multiplying vectors (and matrices) is covered quite well in thousands of online high-school math tutorials, so there is no point in repeating it all here. Writing code without understanding what it is doing is a guarantee that the code will be buggy.
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