n a local high school, the 10th, 11th, and 12th graders were asked if their shoe size was smaller than a 10, or if their shoe size was greater than or equal to 10. Of the 10th graders, 24 had shoe sizes smaller than 10 and 3 had shoe sizes 10 and up. Of the 11th graders, 19 had shoe sizes smaller than 10 and 5 had shoe sizes 10 and up. Of the 12th graders, 14 had shoe sizes smaller than 10 and 12 had shoe sizes 10 and up. Which of the following matrices could represent this information?

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?