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a = {1, 2, 4, 1}

{1, 2, 4, 1}

b = {2, 5}

{2, 5}

M = {{5, 0}, {2, 5}}

{{5, 0}, {2, 5}}

MM = Inverse[M]

{{1/5, 0}, {-2/25, 1/5}}

q = MM . {1, 4}

{1/5, 18/25}