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Consider the tridiagonal matrix
1. Why do we know that Naive Gaussian Elimination will work to solve the system of equations Ax→ = b→ where
for any
?
2. Solve the system of equations Ax→ = b→ where
using Naive Gaussian elimination
3. How do we know that the eigenvalues of A are all real and distinct before we calculate them?
4. Find the characteristic polynomial of A.
5. Find the eigenvalues of A. Hint: The characteristic polynomial can be easily factored into the product of two linear terms and a quadratic that you use the quadratic formula on.
Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible. (Give your answers in increasing order, to the nearest meter.)
Does study group size affect test performance?
Two weather tracking stations are on the equator 159 miles apart. A weather balloon is located on a bearing of N 38°E from the western station and on a bearing of N 14°E from the eastern station. How far is the balloon from the western station?
Let p represent a statement having a truth value T, q represent a statement having a truth value F, and r represent a statement having a truth value T. Find the truth value for the following:
Which of the four operations on functions do you think is the easiest to perform? What is the most difficult? Explain why by showing examples for each function.
Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundredss of liters) is given by C(x) = x3 -2x2 + 8x + 50
Find a polar equation for the curve represented by the given Cartesian equation. xy = 12.
Find the number of ways to get following card combinations
Which number is compatible to use as a dividend with 7?
Determining the maximum area of a Norman window with the fixed perimeter of 16 feet - Evaluate the dimension of a Norman window of maximum area if the total perimeter is 16 feet.
A manufacture has been selling 1050 television sets a week at 390 dollars each. A market survey indicates that for each 13 -dollar rebate offered to a buyer, the number of sets sold will increase by 130 per week.
Jeremy had a square piece of gift wrapping paper with a side length of x inches that he used to wrap a present. First he cut 6 inches off the right side of the paper and discarded the rectangular scrap. Next he cut 3 inches off the top of the paper..
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