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Chapter 1: Q18E (page 1)
Determine whether the statements that follow are true or false, and justify your answer.
18:
False, because the product of is , which is not same as the given product.
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The reduced row-echelon forms of the augmented matrices of three systems are given here. How many solutions does each system have?
a. Using technology, generate a random matrix A. (The entries may be either single-digit integers or numbers between 0 and 1, depending on the technology you are using.) Find . Repeat this experiment a few times.
b. What does the reduced row-echelon form of most matrices look like? Explain.
The accompanying sketch represents a maze of one-way streets in a city in the United States. The traffic volume through certain blocks during an hour has been measured. Suppose that the vehicles leaving the area during this hour were exactly the same as those entering it.
What can you say about the traffic volume at the four locations indicated by a question mark? Can you figure out exactly how much traffic there was on each block? If not, describe one possible scenario. For each of the four locations, find the highest and the lowest possible traffic volume.
The system isinconsistent
Consider the equations
whereis an arbitrary constant.
a. For which values of the constant does this system have a unique solution?
b. When is there no solution?
c. When are there infinitely many solutions?
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