Using congruence axiom 1 prove that If A-B-C then ABAC, AB>AC or AC>AB
Using congruence axiom 1 prove that If A-B-C then ABAC, AB>AC or AC>AB
Prove Congruence Property 3 C3 If a=b (mod m) and c < 1, then ac = bc (mod mc)
(a) If A is invertible and AB = AC, prove quickly that B = C. (b) If A-| | find two different matrices such that AB = AC.
Prove the following using appropriate methods. 10) a AC + AB + BC = AB + BC + AC b. AC + BC + AB EBC + AB+ AC
9. a) Prove that ifA is invertible and AB-AC then B = C.
26) Prove that if A is a nonsing AB = AC, then B = C. Your pro a nonsingular nxn matrix, and B and C are nxk matrices such that c. Your proof must be complete. (10 points) Proof:
24. Can you use the ASA postulate, the AAS theorem, or both to prove the congruence of the triangles? a) either ALA or AAL b) ALA only c) AAL only d) neither 25. What else you should know to demonstrate the congruence of the triangles by ASA? And by SAS? B D a. ZACD = ZCAB, AB CD b. ZACD = ZCAB, AD = BC c. ZADC ZCAB; AD BC d. ZACD = ZCAB, AD 3 AC
1. (a) Prove by algebraic method that ¯a + ab + ac¯+ a ¯bc¯ = ¯a + ¯b + ¯c. (b) Find the CPOS of f(x, y, z) = (x + ¯y)y + ¯xz + x + y + ¯y(x + z).
Prove by algebraic method that a ̄ + ab + ac ̄ + a ̄bc ̄ = a ̄ + ̄b + c ̄.
5. Prove or disprove the following statements (a) Let A B and C be 2 x 2 matrices. If AB = AC, then B = C (b) If Bvi,.., Bvh} is a then vi, . ., vk} is a linearly independent set in R". linearly independent set in R* where B is a kx n matrix, 5. Prove or disprove the following statements (a) Let A B and C be 2 x 2 matrices. If AB = AC, then B...
Simplify Y = AB’ + (A’ + B)C. a) AB’ + C b) AB + AC c) A’B + AC’ d) AB + A