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Show that v is an eigenvector of A and find the corresponding eigenvalue.
Show that lamda is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue.
8. A = [ 2 2, 2 -1], lamda = -2
10. A = [0 4, -1 5]; lamda = 4
Use the method of Example 4.5 to find all of the eigenvalues of the matrix A. Give bases for each of the corresponding eigenspaces. Illustrate the eigenspaces and the effect of multiplying eigenvectors by A as in figure 4.8.
24. A = [ 2 4; 6 0];
26. A = [ 1 2; -2 3].
The solution shows detailed steps of finding the eigenvalues and corresponding eigenvectors of a matrix. It also illustrates the effect of multiplying eigenvectors by the matrix graphically.