A square matrix is called idempotent if (we write to represent ). Suppose that ( ) is a matrix such that is invertible. Prove that both and I_n-〖X〈X^' X〉〗^(-1) X^' are idempotent. (Hint: use this property of matrix multiplication: ).

Abag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue

Plz a. s. a. p. the table shows the number of male and female contestants who did not win a prize. what is the probability that a randomly selected contestant won a prize, given that the contestant was female? write the probability as a percent. round to the neares tenth, if needed.

Haruka hiked several kilometers in the morning. she hiked only 66 kilometers in the afternoon, which was 25% less than she had hiked in the morning. how many kilometers did haruka hike in all?