Consider the given matrix. -1 0 5 4 4 1 4 find the eigenvalues. (enter your answers as a comma-separated list.) 4-i,4,4 i find the eigenvectors. (enter your answers in order of the corresponding eigenvalues, from smallest to largest by real part, then by imaginary part.) -1 1 -8 0 5 k1 = k2= k3 1 i 1 x

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?