Question: 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

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.

4 -1 %3D

Figure 4.8

y 4 - Ax = 4x Ay = 2y У х -4 -3 -2 -1 1 2 3 -1+ -2+ -3+ -4- 3. 2.

4 -1 %3D y 4 - Ax = 4x Ay = 2y -4 -3 -2 -1 1 2 3 -1+ -2+ -3+ -4- 3. 2.

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