- A Let A Be A 3 3 Matrix Assume That The Matrix A Has Eigenvalues 1 1 And 2 With Corresponding Eigenvectors 1 12 1 (161.86 KiB) Viewed 22 times
a) Let A be a 3×3 matrix. Assume that the matrix A has eigenvalues −1,1 and 2 with corresponding eigenvectors ⎝⎛1−12⎠⎞
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a) Let A be a 3×3 matrix. Assume that the matrix A has eigenvalues −1,1 and 2 with corresponding eigenvectors ⎝⎛1−12⎠⎞
a) Let A be a 3×3 matrix. Assume that the matrix A has eigenvalues −1,1 and 2 with corresponding eigenvectors ⎝⎛1−12⎠⎞,⎝⎛110⎠⎞ and ⎝⎛111⎠⎞. Write down a diagonal matrix D and a matrix P such that P−1AP=D. b) Consider the matrix A=⎣⎡1000−2303−2⎦⎤. (i) Find the characteristic polynomial of the matrix A and hence show that its eigenvalues are 1 and −5. (ii) Find a basis for the eigenspace corresponding to the eigenvalue λ=1.
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