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: ).

This race was first held in 1953 on august 16th. every decade the race finishes with a festival. how many years is this?

Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.

Define multiplicative inverse. give an example of a number and its multiplicative inverse.