The trace of a square n x n matrix a = (a_ij) is the sum a11 + a22 ++ ann of the entries on its main diagonal. let v be the vector space of all 2 x 2 matrices with real entries. let h be the set of all 2 x 2 matrices with real entries that have trace 0. is h a subspace of the vector space v? is h closed under addition? if it is, enter closed. if it is not, enter two matrices in h whose sum is not in h, using a comma separated list and syntax such as ,, , for the answer [1324],[5768]. (hint: to show that h is not closed under addition, it is sufficient to find two idempotent matrices and such that +≠+

Subspace; Closed

Step-by-step explanation:

The trace of a square n x n matrix is the sum of the entries on its main diagonal.

Let V be the vector space of all 2 x 2 matrices with real entries.

Let H be the set of all 2 x 2 matrices with real entries that have trace 0.

Theorem: H is a subspace of the vector space V, if

1) for every

2) for each and

Check these two conditions:

1) Let

This means

Consider the matrix

This matrix sum has the trace

So,

2) Consider

Its trace is

So,

Therefore, H is a subspace of the vector space V and is closed under addition.

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

probably .5

i can on others if necessary.