Assume that the nullspace of L = {0}. Explain how it follows that the nullspace of M is {0}? How does it follow that the equation L(X) = Y has at least one solution for all Y ∈  ? Hint: First explain why M is an n × n matrix.

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

Which of the following correctly justifies statement four of the two column proof? a. corresponding angles theorem b. transitive property of equality c. vertical angle theorem d. substitution property of equality

Do xuan nam isgoing to invest $1000 at a simple interest rate of 4% how long will it take for the investment to be worth $1040?