What am I doing wrong? Matrix operators

function surfaceArea = surfaceBalloon(Volume,M)
    
    % Your code goes here %
    radius = ((3*Volume)./((2+M)*pi))^1/3;
    surfaceArea = pi*radius^2.*(2+sqrt(1+M^2));
    
end

What is wrong with my code? It says:

Error using ^ (line 51)

Incorrect dimensions for raising a matrix to a power. Check that the

matrix is square and the power is a scalar. To perform elementwise

matrix powers, use '.^'.

Error in surfaceBalloon (line 5)

surfaceArea = pi*radius^2.*(2+sqrt(1+M^2));

I thought you didn't have to use dot operators unless you are multiplying, dividing, or raising two matricies. I am raising the radius variable to 1/3 which is a scalar value. Am i missing something?

[Stephen23]

"Am i missing something?"

The difference between matrix and array operations.

"I thought you didn't have to use dot operators unless you are multiplying, dividing, or raising two matricies. I am raising the radius variable to 1/3 which is a scalar value."

I don't think that rule-of-thumb is correct. Instead:

• use matrix operations when doing linear algebra,
• otherwise use array operations.

Because, as the documentation makes clear, matrix operations apply the rules of linear algebra.

[Preet Talati]

You need to add a dot operator to all the exponent calculations and your 1/3 needs to be (1/3).

Answer 1

[Star Strider]

If you want to raaise the elements of a matrix to a power, use element-wise exponentiation with the dot operator: .^ and see: Array vs. Matrix Operations for details.

Matrix exponentiation (and several other operattions) are only defined for square matrices. See the Wikipedia article on the Cayley-Hamilton theorem for that discussion.