Question
Asked Nov 5, 2019

Linear algebra

(1) For the matrix A below, find 2 x 2 matrices P, B such that P-1 AP
(canonical) form.
B and B is in Jordan normal
-4 4
(0)
A =
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(1) For the matrix A below, find 2 x 2 matrices P, B such that P-1 AP (canonical) form. B and B is in Jordan normal -4 4 (0) A =

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Expert Answer

Step 1

To transform the given matrix into Jordan canonical form

Step 2

Eigenvalues and eigenvectors of the given matrix A; note that the eigenvalue -2 is repeated (twice) but there is only one linearly independent eigenvector. Therefore the matrix A is not diagonalizable. 

4]
eigenvalues equation
-1 0
4
A
-4-c
4
det(A-cI) 0>det
-1
c+4c+4 (c+2) = 0,c =-2,-2
eigenvector given by
-42 4
х
х
-1
х
x2yChoose
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4] eigenvalues equation -1 0 4 A -4-c 4 det(A-cI) 0>det -1 c+4c+4 (c+2) = 0,c =-2,-2 eigenvector given by -42 4 х х -1 х x2yChoose

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Step 3

To find the matrix P, solve the gene...

generalized eigenvector given by
2 4 x
-1 2
-2x+4y 2.Choose
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generalized eigenvector given by 2 4 x -1 2 -2x+4y 2.Choose

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