Error Using ^ When Typing Power Command

I want to plot a graph of y versus t with:

>> t = linspace(0,10,20);
>> y = 1/(t*(3/10^(8*8)*10^(3/2))/2 + 1)^(2/3);

But when I finished writing the second line, the error appeared: Error using ^ One argument must be a square matrix and the other must be a scalar. Use POWER (.^) for elementwise power. So how can I solve this problem?

[Stephen23]

Why not do EXACTLY what the error message advises you to do?

Read this to know the difference between ^ and .^:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

Answer 1

[Elias Gule]

Let's say for example you have the vector:

t = 1 : 10;

This is basically a 1-by-10 matrix. So,

t^2

tries to perform the matrix multiplication operation; but t is 1x10, hence the inner dimensions of t*t are not the same. That is why you get an error.

Now if what you actually want is an array of squares of elements of t, then

t.^2

is the what you must use. So you equation should be :

y = 1./(t*(3/10^(8*8)*10^(3/2))/2 + 1).^(2/3);

Note: ./, .* and .^ are element-wise operators.

[Duong Nguyen]

Thank you for your explanation. I have just studied MATLAB for a week so I do not understand it fully. It is a really helpful comment.