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HW algebra 2 matrix

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1 Find the determinant of the matrices 1 3 A= 2  1 4 B= 2 0 −1   − 3  0 7  A group took a trip on a bus, at $3 per child and $3.20 per adult for a total of $118.40 They took the train back at $3.50 per child and $3.60 per adult for a total of $135.20 How many children and how many adults? Find the characteristic polynomial and the real eigenvalues of the matrix a b c d Find the (3,2)-cofactor of the matrix  2  −1  a  −2  ; b      3 −  , find matrix P so that P −1 AP is diagonal  5  Let A =  Find a formula for xk if x0 = 0; x1 = 1; xk + = 10 xk − 3xk +1 Solve the following linear recurrences: xk + = xk − xk +1 ; x0 = 1; x1 =

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