Few Urgent Linear Algebra Questions

1. **Determine which of the following formulas hold for all invertible nxn matrices A and B**

a. A+B is invertible

b. (I - A)(I + A) = I - A^2

c. A^9 is invertible

d. (A + A^-1)^3 = A^3 + A^-3

e. AB = BA

f. (A+B)^2 = A^2 + B^2 + 2AB

2. **Determine the dimensions of the following subspaces of R^2 respectively R^3**

1. R^3= span{(-2, -12, 10), (-1, 3, -4), (2, 3, -1)}

2. R^2= span{(–4, –2), (2, 0), (5, 0), (9, –1), (–2, 3)}

3. R^2= span{(7, –2), (–6, 5)}

4. R^2= span{(0, 0)}

5. R^3= span{(–20, –4, 8), (–1, –4, –2), (10, 2, –4), (–4, 3, 4)}

6. R^2= span{(2, –5, –7), (–6, 7, –8), (4, 8, –2)}