Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3
Question
Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3
Solution
Two matrices A and B are said to be similar if there exists an invertible matrix P such that B = P^-1 * A * P.
Given matrices A and B are:
A = [2 0 0; 0 1 0; 0 0 3] B = [1 0 0; 0 2 0; 0 0 3]
We can see that the diagonal elements of A and B are not the same, which means that A and B are not similar. Therefore, it is IMPOSSIBLE to find a matrix P such that B = P^-1 * A * P.
Similar Questions
Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3
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Suppose two n × n matrices A and B are similar.(a) (8 pts) Show that A and B have the same eigenvalues
Use the fact that matrices A and B are row-equivalent.A = −2 −5 8 0 −17 1 3 −5 1 5−5 −9 13 7 −671 7 −13 5 −3B = 1 0 1 0 1 0 1 −2 0 30 0 0 1 −50 0 0 0 0
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