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Algebra 2SuperchallengeLinear Systems & Matrices

Linear Systems & Matrices · Superchallenge problem

Two sequences start with a0=1a_0 = 1, b0=0b_0 = 0 and satisfy

[an+1bn+1]=[3212][anbn]\begin{bmatrix} a_{n+1} \\ b_{n+1} \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 1 & 2 \end{bmatrix}\begin{bmatrix} a_n \\ b_n \end{bmatrix}

for every n≥0n \ge 0. Find a20−b20a_{20} - b_{20}.