Problem 1- Explain what a basis for a vector space is.
Problem 2- Find the eigenvectors and eigenvalues of the following matrix. Write the matrix of eigenvectors and state its rank. If possible, invert it and show that P-1AP = Λ
Problem 3- Find the eigenvectors and eigenvalues of the following matrix. Write the matrix of eigenvectors and state its rank. If
possible, invert it and show that P-1AP = Λ
Problem 4- Find the eigenvectors and eigenvalues of the following matrix. Write the matrix of eigenvectors and state its rank. If
possible, invert it and show that P-1AP = Λ
Problem 5- Use Gram-Schmidt process to compute an orthogonal basis for the following set of vectors. Use the first vector as a starting point for the orthonormal basis that you find:[1 1 1 1] [ 1 2 4 5 ] [1 -3 -4 2]
Problem 6- Find the eigenvectors and eigenvalues of the following matrix. Write the matrix of eigenvectors and state its rank. If
possible, invert it and show that P-1AP = Λ
Problem 7- Use Gram-Schmidt process to compute an orthogonal basis for the following set of vectors. Use the first vector as a starting point for the orthonormal basis that you find: [1 -1 1] [ 1 0 1] [ 1 1 2]
Problem 8- Find the eigenvectors and eigenvalues of the following matrix. Write the matrix of eigenvectors and state its rank. If
possible, invert it and show that P-1AP = Λ
