A, P and D are n x n matrices.

Check the true statements below:

O if A is diagonalizable, then A is invertible.

O A is diagonalizable if A = PDP^-1 for some diagonal matrix D and some invertible matrix P.

O A is diagonalizable if and only if A has n eigenvalues, counting multiplicities.

O Is there exits a basis for R^n consisting entirely of eigenvectors of A, then A is diagonalizable.

In the final round of trivia competition, contestants were asked to name as many states that begin with the letter m as they could in 15 seconds. the bar graph shows the number of states the contestants were able to name. how many contestants participated in the final round of the competition?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

What number is 7 units left of -15?