Please Answer True Or False. No Need For Explanation. Thank You Very Much!!!

3. Let A and B be two square matrices over a field F. Assume that A and B have the same characteristic polynomial. Assume that A is diagonalizable over F. Then, B is also diagonalizable over F. True O False D Question 4 4 pts Let T : RR2 - R2 be the rotation map of angle . Then T has no eigenvectors. O True O False9. If the n x n homogenous linear system Ax=0 over a field F has a unique solution, then the matrix A is invertible. O True False D Question 10 4 pts 10. Let u and v be two eigenvectors of a linear map T with eigenvalues 1 and 2 respectively. Then, u and v are linearly independent. O True O False4 pts 5. Let be an n x n square matrix over a field F. Assume that A has rank r. Then, A has at least nor linearly independent eigenvectors. O True O False Question 6 4 pts 6. An n x n square matrix A over a field F is diagonalizable if and only if its transpose At is diagonalizable over F. O True O Falsepartial credits for Problems 11-16. D Question 1 4 pts 1. Let L and W be two subspaces of a vector space V over a field F. Assume that the intersection of L and W is the zero vector space. Then dim(L+W) = dim(L) + dim(W). O True O False 4 pts Question 2Question 2 4 pts 2. Let p(t) be the characteristic polynomial of an n x n square matrix over a field F. Assume that the polynomial p(t) splits as a product of n linear factors over F. Then the matrix A is diagonalizable over F. O True O False hp4 pts 7. All elementary matrices are diagonalizable over the complex numbers C . True O False D Question 8 4 pts 8. A square matrix A over a field F is invertible if and only if A is a finite product of elementary matrices. True OFalse