Suppose a 3 x 5 matrix a has three pivot columns and a pivot postion in the fifth column. which of the following statements are always true. be prepared to justify your answer.
a) if a is the augmented matrix for a system then the system is consistent with a unique solution.
b) if a is the augmented matrix for a system then the system is consistent with many solutions.
c) if a is the augmented matrix for a system then the system is inconsistent.
d) if a is the coeffient matrix for a system then the system is consistent and has a unique solution.
e) if a is the coefficient matrix for a system then the system is consistent and has many solutions.
f) if a is the coefficent matrix for a system then the system is inconsistent.

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?