MATLAB: Matrix dimension must agree

matrix dimension

i want to calculate values for the vector v, where v=a+b, at time t=0s to t=40s increasing at 0.4 second intervals. b=[0,0,10-(t/4).^2] a=[20.*sin(t),20.*cos(t),0]. but when i populate these values and try and get values for v it keeps saying matrix dimensions must agree.
>> t=[0:0.4:40]
t =
Columns 1 through 12
         0    0.4000    0.8000    1.2000    1.6000    2.0000    2.4000    2.8000    3.2000    3.6000    4.0000    4.4000
Columns 13 through 24
    4.8000    5.2000    5.6000    6.0000    6.4000    6.8000    7.2000    7.6000    8.0000    8.4000    8.8000    9.2000
Columns 25 through 36
    9.6000   10.0000   10.4000   10.8000   11.2000   11.6000   12.0000   12.4000   12.8000   13.2000   13.6000   14.0000
Columns 37 through 48
   14.4000   14.8000   15.2000   15.6000   16.0000   16.4000   16.8000   17.2000   17.6000   18.0000   18.4000   18.8000
Columns 49 through 60
   19.2000   19.6000   20.0000   20.4000   20.8000   21.2000   21.6000   22.0000   22.4000   22.8000   23.2000   23.6000
Columns 61 through 72
   24.0000   24.4000   24.8000   25.2000   25.6000   26.0000   26.4000   26.8000   27.2000   27.6000   28.0000   28.4000
Columns 73 through 84
   28.8000   29.2000   29.6000   30.0000   30.4000   30.8000   31.2000   31.6000   32.0000   32.4000   32.8000   33.2000
Columns 85 through 96
   33.6000   34.0000   34.4000   34.8000   35.2000   35.6000   36.0000   36.4000   36.8000   37.2000   37.6000   38.0000
Columns 97 through 101
   38.4000   38.8000   39.2000   39.6000   40.0000
>> b=[0,0,10-(t/4).^2]
b =
Columns 1 through 12
         0         0   10.0000    9.9900    9.9600    9.9100    9.8400    9.7500    9.6400    9.5100    9.3600    9.1900
Columns 13 through 24
    9.0000    8.7900    8.5600    8.3100    8.0400    7.7500    7.4400    7.1100    6.7600    6.3900    6.0000    5.5900
Columns 25 through 36
    5.1600    4.7100    4.2400    3.7500    3.2400    2.7100    2.1600    1.5900    1.0000    0.3900   -0.2400   -0.8900
Columns 37 through 48
   -1.5600   -2.2500   -2.9600   -3.6900   -4.4400   -5.2100   -6.0000   -6.8100   -7.6400   -8.4900   -9.3600  -10.2500
Columns 49 through 60
-11.1600  -12.0900  -13.0400  -14.0100  -15.0000  -16.0100  -17.0400  -18.0900  -19.1600  -20.2500  -21.3600  -22.4900
Columns 61 through 72
-23.6400  -24.8100  -26.0000  -27.2100  -28.4400  -29.6900  -30.9600  -32.2500  -33.5600  -34.8900  -36.2400  -37.6100
Columns 73 through 84
-39.0000  -40.4100  -41.8400  -43.2900  -44.7600  -46.2500  -47.7600  -49.2900  -50.8400  -52.4100  -54.0000  -55.6100
Columns 85 through 96
-57.2400  -58.8900  -60.5600  -62.2500  -63.9600  -65.6900  -67.4400  -69.2100  -71.0000  -72.8100  -74.6400  -76.4900
Columns 97 through 103
-78.3600  -80.2500  -82.1600  -84.0900  -86.0400  -88.0100  -90.0000
>> a=[20.*sin(t),20.*cos(t),0]
a =
Columns 1 through 12
         0    7.7884   14.3471   18.6408   19.9915   18.1859   13.5093    6.6998   -1.1675   -8.8504  -15.1360  -19.0320
Columns 13 through 24
-19.9233  -17.6691  -12.6253   -5.5883    2.3310    9.8823   15.8734   19.3584   19.7872   17.0920   11.6983    4.4578
Columns 25 through 36
   -3.4865  -10.8804  -16.5565  -19.6187  -19.5836  -16.4566  -10.7315   -3.3121    4.6302   11.8415   17.1832   19.8121
Columns 37 through 48
   19.3132   15.7650    9.7280    2.1551   -5.7581  -12.7621  -17.7513  -19.9380  -18.9769  -15.0197   -8.6913   -0.9907
Columns 49 through 60
    6.8663   13.6393   18.2589   19.9959   18.5759   14.2232    7.6250   -0.1770   -7.9511  -14.4699  -18.7042  -19.9855
Columns 61 through 72
-18.1116  -13.3782   -6.5327    1.3442    9.0088   15.2512   19.0857   19.9070   17.5855   12.4875    5.4181   -2.5067
Columns 73 through 84
-10.0358  -15.9804  -19.4021  -19.7606  -16.9994  -11.5543   -4.2851    3.6607   11.0285   16.6552   19.6524   19.5469
Columns 85 through 96
   16.3553   10.5817    3.1374   -4.8022  -11.9837  -17.2731  -19.8356  -19.2664  -15.6555   -9.5729   -1.9790    5.9274
Columns 97 through 108
   12.8979   17.8322   19.9511   18.9203   14.9023   20.0000   18.4212   13.9341    7.2472   -0.5840   -8.3229  -14.7479
Columns 109 through 120
-18.8444  -19.9659  -17.9352  -13.0729   -6.1467    1.7500    9.3703   15.5113   19.2034   19.8637   17.3879   12.1670
Columns 121 through 132
    5.0252   -2.9100  -10.3858  -16.2219  -19.4969  -19.6938  -16.7814  -11.2197   -3.8866    4.0601   11.3658   16.8771
Columns 133 through 144
   19.7238   19.4567   16.1177   10.2341    2.7347   -5.1963  -12.3070  -17.4747  -19.8836  -19.1532  -15.3990   -9.2136
Columns 145 through 156
   -1.5736    6.3149   13.2063   18.0128   19.9754   18.7844   14.6277    8.1616    0.4070   -7.4119  -14.0606  -18.4894
Columns 157 through 168
-19.9992  -18.3516  -13.8066   -7.0819    0.7609    8.4836   14.8669   18.9030   19.9548   17.8561   12.9384    5.9780
Columns 169 through 180
   -1.9263   -9.5264  -15.6225  -19.2521  -19.8423  -17.2998  -12.0260   -4.8537    3.0850   10.5367   16.3248   19.5356
Columns 181 through 192
   19.6621   16.6845   11.0727    3.7128   -4.2333  -11.5110  -16.9714  -19.7524  -19.4149  -16.0122  -10.0816   -2.5593
Columns 193 through 203
    5.3671   12.4461   17.5602   19.9018   19.1015   15.2854    9.0561    1.3970   -6.4826  -13.3388         0
>> v=a+b Matrix dimensions must agree.

Best Answer

Adding the ‘0’ elements in ‘a’ and ‘b’ are causing the problem, as well as horizontally concatenating the sin and cos terms in ‘b’.
Correcting those problems and vertically concatenating the sin and cos terms in ‘b’, and this works:
t = [0:0.4:40];
b = 10-(t/4).^2;
a = [20.*sin(t); 20.*cos(t)];
v = bsxfun(@plus, a, b);
NOTE — With R2016b (if I remember correctly) and later, you will not need the bsxfun call. I include it here for comaptibility.
Related Question