Reference no: EM131023263
Question 1
Consider the vectors
a = (0, 3, -2, 1, 4); b = (5, 2, 1, 0, -1); c = (7, -3, 6, 21, 0)
(a) Find the length of the vector v = 2a - b;
(b) Are are of the given three vectors parallel or orthogonal? Indicate which (if any).
Question 2
Show that the vectors (1, 2, -1, 4), (0, 1, 0 , -1), (1, 3, -1, 1), (-2, -4, 2, -1) are linearly dependent.
Question 3
Find all eigenvalues and eigenvectors of the matrix
A = [5 8/3 -2/3; 2 2/3 4/3; -4 -4/3 -8/3]
Show your work.
Question 4
Write a paragraph answering each of the following questions.
(a) In solving a typical eigenvalue problem, what is given and what is sought?
(b) What is diagonalisation of a matrix? Describe how diagonalisation helps to solve systems of linear differential equations.
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Compute the total sales dollars to be reported
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Find all eigenvalues and eigenvectors of the matrix
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Is smoking status
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