3. Using propositions aided by two-column proof, show that AAB = AUB. (Just choose one direction to exhibit.) 4. Using laws of set theory aided by two-column proof, show that AU(B-C) (AUB)-(C- A).

Q: 1 -3 4 1 Let A = 1 2 -3 2 4. B = -4 0 -2 [-1 2 5. Find Rank of AB

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Q: 2. Determine the products C = AB and D = BA if 4 67 -7 -5 A = -1 3 -5 21 -13 -4 7 6 %3D 1 -9 -3 1

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Q: 2 2 -2 If A = = -1 0 3 -4 -4 and B -2 0 th 1 -3 3A – 2B and 4AT 24

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Q: 2. Find u, 3v, v-u, and 2u +5v. 3. u = (5, 3), v = (3, -2) %3D

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Q: 1 2. Can c = 1 be written as a linear combination of a1, a2, a3 ? explain why or 1 why not?

A: Step 1:

Q: 4x1 -5x2 +2x3 +2x4 +x2 +3x3 -4x2 +5x3 +4x4 -X1 +2x4 = 4 3x1 -2x1 +2x2 +6x3 +4x4 8 X1 X2 +s +t X3 X4

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Q: 4 4.x1 -3x2 +2x3 +4x4 = +x2 +2x3 +2x4 -2x2 +4x3 +6x4 = 10 3x1 -2x1 +2x2 +4x3 +4x4 = x2 +s +t %3D x3

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Q: G (5,8) H (4,-5) J (17,-6)

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Q: The following is known about three numbers: Three times the first number plus the second number plus…

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