)determine elementary matrices e1, e2, e3 of type iii such that e3e2e1a = u with u an upper triangular matrix. the matrix e1 should turn the element in position (2,1) into a 0. enter this matrix in matlab as e1 using commands similar to the ones in example 1. the matrix e2 should turn the element in position (3,1) into a zero. enter this matrix in matlab as e2. note that to zero out the entries in column 1, you need to add or subtract a multiple of row 1. once you have found the matrices e1 and e2, compute the product e2e1a in matlab. use format rat so that the entries will be given as fractions. based on the result, determine the matrix e3 that turns the

Signal sets company contracts to deliver one hundred 52-inch plasma high-definition television sets to a new retail customer, tuner tv store, on may 1, with payment to be made on delivery. signal tenders delivery in its own truck. tuner's manager notices that some of the cartons have scrape marks. tuner's owner phones signal's office and asks whether the sets might have been damaged as they were being loaded. signal assures tuner that the sets are in perfect condition. tuner tenders signal a check, which signal refuses, claiming that the first delivery to new customers is always for cash. tuner promises to pay the cash within two days. signal leaves the sets with tuner, which stores them in its warehouse pending its "grand opening sale" on may 15. two days later, tuner's stocker opens some of the cartons and discovers that a number of the sets are damaged beyond ordinary repair. signal claims tuner has accepted the sets and is in breach by not paying on delivery. will signal succeed on these claims? explain.

Write a program called assignment3 (saved in a file assignment3.java) that computes the greatest common divisor of two given integers. one of the oldest numerical algorithms was described by the greek mathematician, euclid, in 300 b.c. it is a simple but very e↵ective algorithm that computes the greatest common divisor of two given integers. for instance, given integers 24 and 18, the greatest common divisor is 6, because 6 is the largest integer that divides evenly into both 24 and 18. we will denote the greatest common divisor of x and y as gcd(x, y). the algorithm is based on the clever idea that the gcd(x, y) = gcd(x ! y, y) if x > = y and gcd(x, y) = gcd(x, y ! x) if x < y. the algorithm consists of a series of steps (loop iterations) where the “larger” integer is replaced by the di↵erence of the larger and smaller integer. this continues until the two values are equal. that is then the gcd.

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