10/23/2023 0 Comments Matrix a^2![]() ![]() ![]() As a quick check, see that this fits our first equation, a = 3 = a 2 + bc = 9 – 6. Now -2 = bc + 4, by our a last equation above, so -6 = bc. ![]() To come up with your own idempotent matrix, start by choosing any value of a. Since A 2 = A, we know that for a matrix ,ī = ab + bd, so b – ab – bd = 0 and b(1 – a – d) = 0 and either b = 0 or d = 1 – aĬ = ca + cd, so c – ca – cd = 0 and c(1 – a – d) = 0 and either c = 0 or d = 1 – a Nontrivial examples of 2 x 2 matrices are relatively easy to come up with ( Need help? Check out our tutoring page!). The simplest examples of n x n idempotent matrices are the identity matrix I n, and the null matrix (where every entry on the matrix is 0). An idempotent matrix is one which, when multiplied by itself, doesn’t change.
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