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Give an example which shows that in the matrix chain multiplication problem, adding a matrix on the right can force the breakpoint to the left. You can find an example using just 4 matrices. This shows that the trick used to speed up optimal binary search tree computation cannot be used for matrix chain multiplication.
Six people are going to travel to Mexico City by car. There are six seats available in the car. In how many different ways can the six people be seated in the car if only three of them can drive?
Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A.
Let F be a forest. Add a vertex x to F and join x to each vertex of odd degree in F. Prove that the graph obtained in this way is randomly Eulerian from x
Find the best unbiased point estimate for the population mean weight of the packages received by the parcel service.
I wish to find the general nontrivial solution to the fourth order ODE with boundary conditions
An ad for a computer printer stated that you could buy the printer for only $280.00, or 80 % of the original price . What was the original price of the printer?
Using the optimistic and conservative approaches in a decision analysis will never give the same optimal decision is the question true or false?
Find the score that marks the top 5 percent
One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742. The conjecture made in this letter is now known as Goldbach's Conjecture. The conjecture is as follows:
To pour a concrete sidewalk takes 2 hours of preparation nd 3 hours of finishing. To pour a concrete patio takes 4 hours of preparation and 3 hours of finishing. ABC Concrete Company makes a profit of $450 on a sidewalks and $700 on a patio.
In one room of the science fair were six projects, and each project was entered by a pair of students. During the fair, some of the students visited other projects in the room and shook hands with some of the other project entrants.
The form of augmented matrices.
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