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SpringPhysics
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Homework Statement
Suppose A is a 2x2 real matrix with characteristic polynomial f(t) = t2 - 5t +4. Find a real polynomial g(t) of degree 1 such that (g(A))2 = A.
Suppose A is a 2x2 complex matrix with A2 ≠ O. Show that there is a complex polynomial g(t) of degree 1 such that (g(A))2 = A.
Homework Equations
Cayley-Hamilton Theorem
The Attempt at a Solution
I found that det A = 4 and from f(A) = 0, I found the inverse of A to be 1/4 * A(A-5).
I am completely stuck after this. I let A be a matrix of 4 variables a, b, c, and d, then tried to solve for the variables but ended up with really long and messy terms.
Can someone give me a lead as to what the g(t) has to do with f(t)?