We know from Table 1 that similar matrices have the same rank. Show that the converse is
Chapter 5, Problem 23(choose chapter or problem)
We know from Table 1 that similar matrices have the same rank. Show that the converse is false by showing that the matrices A = 1 0 0 0 and B = 0 1 0 0 have the same rank but are not similar. [Suggestion: If they were similar, then there would be an invertible 2 2 matrix P for which AP = PB. Show that there is no such matrix.] 24
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