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abstract Boolean algebra addition and multiplication additive identity algebra of sets algebraic system argument assume augmented matrix axioms basis belong binary operation Boolean algebra Boolean function called column vectors commutative complement complex numbers components consists corresponding defined Definition denoted dimensions domain elementary transformation equal equivalence relation example field Figure frequency given Hence Illustration integers inverse linear combination linear transformation linear vector space linearly independent logical propositions m x n matrix maps mathematics matrix game n-tuple nonsingular obtain odd integer ordered pairs player points possible outcomes probability Problem product set Proof properties Prove pure strategy real numbers respectively row vectors sample space scalar multiplication Section set of real Show simple event Special elements statement status vector subset switching circuit symbol Theorem theory true truth table truth value universal set valid vector space write xu x2