If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

Q: verify that (AB)C = A(BC)

A: Given matrices:

Q: 14.Let A= 3+2i 0 2 1+i 1-i B-( + ?) and B= Find AB.

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Q: -25 (1+j2 2-j5 ) = 57 + j24 2 \3+j4

A: We need to simplify the expression -2521+j23+j4-2-j5-j and show that it is equal to 57+j24 Consider,…

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

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Q: If A = (a, b) and B= (b, c), find: (i) (AUB) (ii) (AnB)' (ii) A'UB

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Q: 2. Show that (a) Re(iz) - Im z; = (b) Im(iz) = Rez.

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Q: a2u a2u 2y дхду a²u )Find du where ax - - axây' ay? u = x3 - 2x2 + 2y3 – 6xy + y ax2

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Q: 2 let -27 Aslo -3 1470 -4 find AB+BA,AA"AA, (3A=2B)°C A'C..

A: "Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

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Q: 7. f(2) = -3, g(2) = 2, f2) = 4, g(2) = -5 a) If h = 0, use the values above to find h) 9(x)

A: 7. f2=-3, g2=2, f'2=4, g'2=-5

Q: All of the following are equidistant from the point (6,8) EXCEPT о (6, —2) 0 (-2, 12) о (16,8) O…

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Q: (a) A = [í 21 B = R s c= D= -2 -5. 4 = G ) B= = L, ) = 5[ -3 -5 (b) A = [; ) B =[ D = 5 -11. -5]

A: Givena)A=2112, B=-30-2-5 , C=-2-402, D=0000.b)A=1114, B=-3-50-11 ,C=19-110 , D=-55-20-25To find All…

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: Suppose X~N(19, 2.5).  Find P(X = 17)

A: Given X~N(19, 2.5)

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Verify that det(AB) = det(A) det(B) for the following:

A: Given: The given matrices are A=1-23-231010 and B=1023-25213. First, find the determinant of A and…

Q: Consider x = 3x1 – 2x2, x, = 2x1 – 2x2, with x (0) = 3, x2 (0) = ;. b If x1 ge + e-, find the values…

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Q: 1-3у 2у - Зу? 1.

A: Given: ∫1-3y2y-3y2dy

Q: A Find a numbel z That satisfies The condubion g af The MUT I dx= 9 4 -4 O -a 0-15

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Q: 2. Show that 1 2 = (1 - )( - )(? y)

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Q: Simplify: 8x+7 y-10 9xy 11axy 79xy+77y+90x O A. 99xy 79xy+77y+90x 99x²y 90xy+77y+79x 99x y .2 O B.…

A: 8x+79x2y-y-1011xy2=(8x+7)11xy2-(y-10)9x2y9x2y(11xy2)

Q: verify that (A + B)C = AC + BC

A: To verify that (A+B) C = AC + BC.

Q: P → (Q → R) is equivalent to A. (P ^ Q) → R B. (P v Q) → R  C. (P v Q) → ∼R D. None of these

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Q: () - (" ;')-(,".) Show that: n+1

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Q: Ifa' = (-5,1,2) and b' (-1,–2,4)and, find a – 3b.

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Q: у" — бу" + 11у' — бу — 4sin7х + 5 - %3D -

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Q: [2 4 21 A = l1 3 1 1 1 B = -2 -1 [2 4 D = 4 C = 1 3 21 -1 %3D 2

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly  C = AD = -B

Q: In (z z2) =

A: I have provided this answer in step-2.

Q: how did the y' and 2y' apearred out of no where in line 7

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Q: If 1 A = -9 6 1 6. 2 -T and Q(#) = ' Až, then Q(z1, 12, T3) = Enter z1 as x1, 12 as x2, and 13 as…

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Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

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