Using random matrices for practicing eigenvector and eigenvalue questions will often result in non-integer values that...
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Using random matrices for practicing eigenvector and eigenvalue questions will often result in non-integer values that are confusing and tedious to calculate. Use the following to reverse engineer a question. i. Give three simple, linearly independent column vectors X₁, X2, X3 € R³. Ensure that they each have at least 2 non-zero entries, and that one of your values is negative. (these are your eigenvectors) ii. Pick three eigenvalues, A₁, A2, A3. Use integer values, and have one of your A, such that A₁ <0. iii. We know that Ax= Ax for each of your eigenvectors. Hence set up a system AX = B where X = [X1X2X3] is the matrix with your eigenvectors as columns, and solve for A. 5 marks Using random matrices for practicing eigenvector and eigenvalue questions will often result in non-integer values that are confusing and tedious to calculate. Use the following to reverse engineer a question. i. Give three simple, linearly independent column vectors X₁, X2, X3 € R³. Ensure that they each have at least 2 non-zero entries, and that one of your values is negative. (these are your eigenvectors) ii. Pick three eigenvalues, A₁, A2, A3. Use integer values, and have one of your A, such that A₁ <0. iii. We know that Ax= Ax for each of your eigenvectors. Hence set up a system AX = B where X = [X1X2X3] is the matrix with your eigenvectors as columns, and solve for A. 5 marks
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Related Book For
Corporate Finance
ISBN: 978-0077861759
10th edition
Authors: Stephen Ross, Randolph Westerfield, Jeffrey Jaffe
Posted Date:
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