true or false

1. If A' equals the zero matrix, then A is the zero matrix. 2. If det(AB) = det(AC) and A is not invertible, then det B = det C. 3. If AB = BA and A is invertible, then A 'B = BA-1. 4. The product first rotates vectors clockwise 90" and then reflects vectors across the r-axis. abc 2a 2b 2c 5. If det de f = 3 then det. 2d 2e 2f = 18. g h i 2g 2h 2i 6. The best approximation to y by elements of a subspace W is given by the vector y - projwy. 7. If A is a 3 x 2 matrix, then AB is not invertible. 8. The columns of a matrix A form a spanning set for Col A. 9. The matrix equation Ax = b has a solution if and only if b is in the column space of A. 10. If H = Span {V1, V2, va}, then {V1, v2, v3} is a basis for H. 11. If { v1, v2} is a linearly independent set in a vector space V, then there exists a basis for V which contains vi and v2. 12. If there exists a linearly independent set { V1, v2, v3} in a finite-dimensional vector space V, then dim V > 3. 13. If x is a least-squares solution of Ax = b, then Ax is the projection of b onto the null space of A. 14. If A = QR is a QR-factorization of A, then Q Q = 1. 15. The rank of a matrix is equal to the number of free variables