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10 Nov 2019
What are the eigenvalues and eigenvectors of F := ? Evaluate F2 and multiply it by the eigenvectors from part (a) to deduce what the eigenvalues of F2 are. Explain what you think the eigenvalues of the square of a matrix will be in general, and use algebra to explain why. Explain why any matrix with determinant 0 will always have eigenvalue 0 too. Calculate the adjoint of this matrix: E := Which value of y guarantees that E has an inverse? Create an always singular matrix including an x and a y and no zeroes. Explain why this cannot be done if the x and y are in different rows and columns.
What are the eigenvalues and eigenvectors of F := ? Evaluate F2 and multiply it by the eigenvectors from part (a) to deduce what the eigenvalues of F2 are. Explain what you think the eigenvalues of the square of a matrix will be in general, and use algebra to explain why. Explain why any matrix with determinant 0 will always have eigenvalue 0 too. Calculate the adjoint of this matrix: E := Which value of y guarantees that E has an inverse? Create an always singular matrix including an x and a y and no zeroes. Explain why this cannot be done if the x and y are in different rows and columns.
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Lelia LubowitzLv2
31 Jan 2019