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Combine from JPE, Fall 90 and Spring 97) Let A ∈ C^(n X n) be a normal matrix.
a. Prove that A - M is normal for any λ ∈ C. Prove that ||Ax||2 - ||∧*x||2 for all x ∈ C^n
b. Prove that ( λ, x) is an eigenpair of A if (λ, x) is an eigenpair of A*. (Hence A and A* have the same eigenvectors.
Explain Bisection and newton's method, Using the bisection method, find the positive root of 2x(1 + x^2)^-1 = arctan x
Using MatLab, compute H^-1H for various n between 5 and 15. Describe the results and comment on the difference between the MatLab output and what is expected the answer to be
Test for independence of attributes
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Calculate the breakeven point
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Calculation involving a change in blood pH. Although the pH of human blood is normally between pH 7.3-7.5, certain situations can take place which bring about "acidosis." Acidosis is defined as an abnormal lowering in the blood pH
Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?
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Ron the realtor is offered a job directly out of real-estate school. he has a selection as to which way he will receive his salary the first year.
What route will take the least amount of time?
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