3 7 1 2. Let A = |2 15 [2 -1 0] B Determine if and C = 5 1 5 0 -1 6 the following are defined, and if so, calculate them. (а) АС (b) ВС (c) AB (d) ВА

Q: [1 2] If A = then show that |2A|=4|A| %3D 4 2

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Q: Find all values of z for which z* + 2 – i2v3 = 0 and represent them geometrically.

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Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: 1 2 If R = 3 1 that R² = 2R + cS. and S= 1 1 0 0 1 find a number c such

A: Solving matrices question by finding square of R matrix

Q: [1 2 [1 2 [1 2 01 Q13: If A = 1 1 0 1 4 ol 3 B = 1 1 -1 l2 2 2 and C = 1 1 -1 Show li 1 1 that AB =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: [1 0 2] 6. If A= 2 -1 3 and B = 3 4 1 8 4 8 -7 9, then prove that (AB) = B" A". -5 0 2 %3D 2.

A: Given:             A=1022-13418 and  B=2483-79-502…

Q: 7. If [G: H] = 2, prove that gH = Hg (18 from 6.5)

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Q: Let  A = (1 1 1, 1 2 2) Find R(A), R(AT), and N(A)

A: Given,A=111122the reduced row echelon form of AMake zeros in column 1 except the entry at row 1,…

Q: 6. Evaluate the det A where A = 1 0 -1 2 4 24 3 1 0 1 0 041 44

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Q: 2.4.3. Let p(r1, T2) = 16, T1 = 1, 2, 3, 4, and r2 joint pmf of X1 and X2. Show that X1 and X2 are…

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Q: 6-8(/2) Ce?: x3+2°<9, x<0?\ ): ト 4,X,c03 and 年(カx2)= (4),6) = (-2x2 , 3w×2) ncludng Sfidx + dr2 = ST…

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Q: 8 (2-15)*- 3-V5 (a) Express in the form p + q5, where p and q are integers. (b) Given that = ab°,…

A: To solve the given problem we use the following result (a - b)2 = a2 + 2ab + b2 , (a+b)(a-b) = a2 -…

Q: 1 0 2 2 4 8 -7 9, then prove that (AB)' = B" A" . -5 0 If A = 2 -1 3 and B : 3 4 1 8 2

A: Evaluate (AB)T as follows.…

Q: Express In (2) in the form a + ib. (Simplify your answer completely.) In(z) = BRITK In( 4√2 ) + 1 (…

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Q: [1 2 [1 2 01 Q13: If A = 1 1 0 li 4 ol [1 2 B = 1 1 -1 and C = 1 1 -1. Show l2 2 3 3 2 li 1 11 that…

A: given matrix

Q: (b) Let a, b, c, xo, x1, Yo, Y1 ER and xo # Yo, a + 0. Then the ODE ay" + by' + cy satisfying y(xo)…

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Q: 3. Prove indirectly. Let Q = {n/m|m,n E Z and m # 0}, and I = R – Q. Ifr e Q and s E I, then 2r – 3s…

A: Here, We'll use method of contradiction to prove the result.

Q: _9. If x is an odd integer, then 2x + 1 is also an odd integer. If 2x + 1 is an odd integer, then…

A: Both the questions are solved below.

Q: Show that e = (1 + i)/√2 if and only if z = (n/4+2km)i, k = 0.±1, +2...

A: This question is related to complex numbers,  we will solve it using given information.

Q: Let A = -[-32-3] and B = (a) Find AB, A-1, and B-1. AB= 5-3 2-1 A-1 B-1 = (b) Show that (AB)-1 =…

A: a)AB=2-2-235-32-1AB=2(5)-2(2)2(-3)+2-2(5)+3(2)-2(-3)-3AB=10-4-6+2-10+66-3AB=[6-4-43]A-1=1AAdj(A)A-1=…

Q: 3.8. Let z and w be such that Zw 1, | z| < 1, and |w| < 1. Prove that 2 - w < 1. 1- Zw Determine…

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Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

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Q: 1The land of Zoo Nearland consists of two islands, the Each year 35% of the populatiou of the East…

A: (a) given let ek and wk be the population of the east and west islands respectively to find  a…

Q: (b) If m < a1 + ... + an < M n, and v, is positive and + anVn < Mv1. + anUn| < Mvi Vn. decreasing,…

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Q: 3 0 -6 ド:3 1 C = 4 2 A = B = %3D %3D 3 1 5 152 D = -1 0 1 6 1 3 1 2 4 1 3 E = -1 | 3 2 4 Compute the…

A: Given matrices are: A=30-12110, , B=4-102, C=142315 D=152-101324, E=613-112413 Now DT=1-13502214,…

Q: 1 2 3 1 that R2 = 2R+cS. b. If R = and S= 1 0 01 find a number c such

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Q: 2 1] Assume A = 1 3 4. [2 2 4 and B = show that (AB)' = B' A' [3 6 4]

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Q: 3. Prove indirectly. Let Q = {n/m | m,n E Z and m # 0}, and I = R – Q. If r e Q and sE I, then 2r –…

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Q: [2 1] Q2) Assume A = |1 3 .3 4] 2 4 1 and B = l show that (AB)' = B' A' 13 6 4] [

A: Here, it is given that  A=211334 and B=241364. We need to show that (AB)'=B'A'

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

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Q: 3. Let A, BE M2(Z3) be given by [1 2] B 0 2 A = 1 Find AB, BA, and A? (recall that A2 = AA).

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Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

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Q: μ = 3, o² = 9, P(-6 < X<12) a. Determine P(u - ko < X <u+ ko) ≥ 1 − 1/k²

A: It is given that Mean = 3 And variance = 9

Q: (-8 1 4 (a) If A = 4 4 7 prove that A- = A' where A' is the transpose of A. 1 -8 4

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Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: [2 and C = |1 1 Let A = [2 0 -1] ,B = -1 %3D 1 Then (2BA - CT) is -1 -21 -4 1 -5 equal to the above…

A: This question is related to linear algebra

Q: 8/14 Let 1 < p < 0. For t = [0, 1], let xi(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2 <t≤1 and for n =…

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Q: 2 11 Q2) Assume A = |1 3 [3 2 4 1 and B = show that (AB)' = B' A' %3D 3 6 4J 4]

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Q: μ = 3, o² = 9, P(-6 < X < 12) a. Determine P(u - ko < X < µ+ ko) ≥ 1 − 1/k²

A: Given μ=3, population variance σ2=9, P(-6&lt;X&lt;12)=?

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: 4.6. Let a e Z. Prove that if 3|2a, then 3|a. 4.7. Let n E Z. Prove that 3 (2n² + 1) if and only if…

A: Let n in Z , then we have to prove that 3 | (2n2 + 1) if and only if 3 doesn't divides n.

Q: 3) Calculate: AВ-ВА , АС-СА , ВС-СВ Where 1 1 0 1 A 1 1 B -1 1 0 0 V2 Vzi 1 0. 0 -1 0. -1

A: I have found each product term one by one

Q: 1. Find all numbers z such that Az' + Bz2 + Cz = D [2 4 2 A = 2 4 2 1 B = 3 1 - 2 3

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

Q: Show ther' 3 2

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Q: 14. Let A = {r € R : 2 < z < 4} and B = {r €R: -4 <I<1}. Prove that |A| = |B|.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.