Vector spaces, closed under addition

[bakin]

Homework Statement

Let
S={A (element) M₂(R) : det(A) = 0}

(b) Give an explicit example illustrating that S is not closed under matrix addition.

Homework Equations

The Attempt at a Solution

1) I think that the problem is saying S is a set of 2x2 matrices, whose determinant is zero?

2) I'm also not exactly sure what it means by "explicit example". What I put down was this:

Is this the right way of approaching it? det(a) is zero, det(b) is zero, so they are members of S. But, adding a and b together gives a new matrix that doesn't have a determinant of zero.

 

[Dick]

I think that's exactly what they were asking for.

 

[bakin]

Pulled through once again, Dick. Thanks for the clarification!