In each case, determine which of axioms P1-P5 fail to hold. (a) V = R2, ((x1,y1),(x2, y2))
Question:
(a) V = R2, ((x1,y1),(x2, y2)) = x1y1x2y2
(b) V = R3 , ((x1, x2, x3),(y1,y2,y3))
= x1y1 -x2y2 + x3y3
(c) V = IR, (z,w) = zw, where w is complex conjugation
(d) V = P3(p(x), q(x)) = p(l)q(l)
(e) V = M22, (A, B) = det (AB)
(f) V = F[0,1], (f, g) = f(l)g(0) + f(0)g(l)
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b P5 fails 0 1 0 0 1 0 1 The other axioms hold Write x x 1 x 2 x 3 y y 1 y 2 y 3 and z z 1 z 2 z ...View the full answer
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