(1 point) a b c Given det d e f = 5, find the following determinants. g h i g h i det a b c de f. a b c 6f + c 6d + a 6e + b 6f + c = g h i 6d + a 6e + b 6f+c d e f = J
Let A. B, C, D є Mnxn(F), and det(A) 0, AC-CA. Prove that A B det ( )) -det(AD CB)
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: A ∪ B 12. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: b. A ∩ B 13. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: AC...
(1 point) a b c If det d e f = 1 ghi a-63 6b - 36h C - 6i then det d be f = g - 6h
Let A={a b c d e f} B={a c e g} C = {b d f} Find each: B = {a, c, e,g} C = {b,d,f} A= {a,b,c,d,e,f} Find: (2 points each) (a) AnB (b) AUB (c) Ang (d) COB (e) CUB (f) (An B)UC (g) An(BUC) (h) Ax B (i) C XB G) AB (k) C ( BA) (1) B2
(1 point) If det b 1 3 and det b 2 e 3 then a 5 det|b 5 el=15 and c 5 f c 8 f (1 point) If det b 1 3 and det b 2 e 3 then a 5 det|b 5 el=15 and c 5 f c 8 f
Let Ω = {a, b, c, d, e, f}. Assume that m(a) = m(b) = 1/16 , and m(c) = m(d) = m(e) = m(f) = 7/32 . Let A, B and C be the events A = {a, d, e}, B = {a, c, e} and C = {a, c, d}. Are A, B, C mutually independent? Explain
Let a T: M2x2(R) + P2(R), 6 d H (2a +b)x2 + (6 – c)x +(c – 3d). с Let B = 9 (6 8), (8 5), (1 3), ( )) (CO 11),( ( 1),66 1 B' 1 1 ? :-)) C = (x²,2,1) C' = (x + 2,2 +3,22 – 2x – 6). 3 Let A 14). Compute [AB (2pt) Enter your answer here and T(A) C (2pt). Enter your answer here
3. Let det(A) = 3 and det B = –2. Find the indicated determinants: (a) det(AB) (b) det(B-1A) (c) det(AAT) (d) det(3BT)
Let us consider V = {a, b, c, d, e} and F = (a ∨ b ∨ c ∨ d ∨ e) ∧ (¬a ∨ ¬b ∨ ¬c ∨ ¬d ∨ ¬e) ∧ (a ∨ ¬b ∨ d ∨ ¬e) ∧ (¬b ∨ c ∨ ¬e) ∧ (¬b ∨ c). a) Is F a 3SAT propositional formula? b) Find a 3SAT propositional formula F’ equivalent to F. c) If you design a polynomial algorithm to find the truth assignments for...