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- Why is it that if I do row expansion on the first row, I get det(A) = -1, but, if I do it in the second row, det(A) = 1. Where did I go wrong?Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]Find the ordinary generating function for the sequence 0,0,0,0,1,1,1...(Hint: it is not a polynomial.)
- how does the a in the second row become a 0Suppose that the number of bacteria in a colony doubles every year. Set up a recurrence relation for the number of bacteria after n hours have elapsed. If 200 bacteria are used to begin a new colony, how many bacteria will be in the colony in 15 hours?Starting with any rectangle, we can create a new and larger rectangle by attaching a square to the longer side. For example, if we start with a 2x5 rectangle, we would attach a 5x5 square to the 5 sides of the original rectangle to obtain a 5x7 sided rectangle; we could then proceed recursively attaching a 7x7 square to this rectangle to obtain a 7x12 sided rectangle. a. Create a sequence of rectangles using this rule starting with a 1x2 rectangle. Then let a_n the sequence of perimeters of these rectangles starting with a0=1+2+1+2=6a0=1+2+1+2=6 b. Do the same for the sequence starting with a 1x3 rectangle. c. Find recursive formulas for both sequences (don't forget the initial conditions) d. Are the sequences arithmetic or geometric? Are they close?
- Also, how do you create a recursion formula?A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he finished 1/n of the job left. On the third day, he finished 1/m of the job left, and on the fourth day, 1/n of the job left. On the last day, he finished 1/4 of the remaining job. find m and n.Suppose that the number of bacteria in a colony triples every hour.a) Set up a recurrence relation for the number of bacteria after n hours have elapsed.b) If 100 bacteria are used to begin a new colony, how many bacteria will be in the colony in 10 hours?
- A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, what is the total weight in tons of all the wheat that will be placed on the first 6464 squares? (Assume that each grain of wheat weighs 1/7000 pound. Remember that 1 tonequals=2000 lbs.)The total weight of the wheat that will be placed on the first 6464 squares is nothingtons.(Use scientific notation. Use the multiplication symbol in the math palette as needed. Do not round until the final answer. Then round to six decimal places as neededSuppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1–3 are to choose the uppercase letters to put in positions 1–3 and the remaining steps are to choose the digits to put in the remaining positions. There are ways to perform steps 1–3, and there are ways to perform the remaining steps. Thus, the number of license plates is . (b) How many license plates could begin with A and end in 0? In this case, the number of ways to place the A in Step 1 is and the number of ways to place the 0 in the final step is . Thus, the answer is . (c) How many license plates could begin with UVA? In this case, the number of ways to perform steps 1–3 is . Thus, the answer is . (d) How many license…A researcher makes observations of certain bacteria. Every 1/2 day the bacteria divide into 2. At the beginning of the observation there were two bacteria. If every 2 days there are 1/4 of the dead bacteria. Find the number of bacteria alive after 3 days