1. Show that ADAC is similar to ABAE (DA) (AE) = (BA) (AC) 2. Show that DA AE

Q: -2 -3 Q3) Find JA| Where A =1 0 1 1 -1

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Q: Solve for the following: a) Var(2X−5) when X ∼ U {1,2,…,20}. b) Var(3X−4) when X ∼ U {1,2,…,30}.

A: Given,X~U(1,2,.....20)minimum value=1maximum value=20f(x)=120-1f(x)=119         ; 1≤X≤20

Q: Compute ATBT and BT AT by hand if possible. If not possible, describe why. A = 2 3 −1 0 B = 10 -1 0…

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Q: L[sih bt) 2.

A: From the definition of Laplace, L(f(t))=Fs=∫0∞fte-stdtSo,L(sin(bt))=∫0∞sin(bt)e-stdt Let,…

Q: c) cuc (sec sx)

A: Given : cos-1(sec5x)

Q: Verify that (AB)T = BTAT.

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Q: Show that we can have: (a) ANB = ANC without B = C. (b) AUB = AUC without B = C.

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Q: Please answer in typing format for like

A: Given : For two events A,B∈Ω,(i) P(B|Ac)= 0.1 (ii)P(Bc|A)= 0.8(iii)P(A)= 0.4Where Ω is the set of…

Q: 2. Simplify the following: 2 (m²)? ii) (62n* 1 ) ( 9 2n) (35+1 ) (2 2) i) ii) (2m³) 2 (3m) 2

A: Topic:- simplification

Q: Find (1+i)5.

A: Need to find .Use Binomial Theorem.

Q: 16) (4xy)*|

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Q: -6 B) [ x In(x) 12

A: First I have used the property of logrithmic and made the integral easy and then by substitution…

Q: ip Prove tan0 = e-ip 2i

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Q: sec* z tan' eda 3 Evaluate

A: Given integral, ∫sec5x tan3x dx

Q: 8. If x = 1- 1 and y = In 1, what is in terms of 1 ? dx (B) 21 (C) -- (A) (D) 212 (E) 214

A: Given x=t2-1,  y=lntdxdt=2t,  dydt=1t Now,  dydx=dydtdxdt=1t2t=12t2

Q: If det (AB²) = 24 and det(AB) = 8, what is det (BT) equal to?

A: Note that, det(AB)=det(A)×det(B)

Q: Calculate principle value of (21) ²¹

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Q: if fcx) = _X then f (-1) is: |-X

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Q: How can I calculate using Excel?   Suppose X~N(193,7), and Z~N(0,1). Then x = 204, is equivalent…

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Q: Sketch the following given that Z = x + yi (2-3) (2+3) = 2

A: Given ,                 (z-3)(z+3) = 2   ;    z=x+iy

Q: re 1 da Ji rVI- (In x)²

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Q: What is TCAsin77° + 2 Tcasin38.7°?

A: This is a problem related to trigonometric function. Here we will put the values of the sin and then…

Q: x+3 dx. 2x -7

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Q: Evaluate: (8t – 121 + 6)dt

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Q: Reduce (1+j)?/(1-j) to the form a+jb. a. others b. -1-j С. 1+] d. 1-j е. -1+j

A: 1+j21-j×1+j1+j=(1+j)31+1=j3+3j2+3j+12=-j-3+3j+12=2j-22=j-1=-1+j

Q: Evaluate iy ( + + " ). Nin t

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Q: 11. Prove (AUB) × C = (A x C) U (B × C)

A: 11 prove (A U B)*C = (A X C) U (B X C) here this is the property of distributive  so this is direct…

Q: Given u = r² cose and v= = rsin²0, please write down the expression of ər 3 and 3 ди by (r, 0)

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Q: What is the value of (V-1)' ? A. e- BỊ e C. e D. e

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Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: (b) у — 2г tan-"(г) — In(1 + x?)

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Q: (a) If j² = -1, simplify

A: (a) if j2=-1, then      (i) j6=

Q: Find the value of S in (3A +4Si)(6-7i) = 3+5i

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Q: (b) Ji 교2(중교" + 1)dr (c) (ax² + bx + c)dx (d) L.(; + ap(뿌

A: Use the formulas below to evaluate the integrals. ∫xndx=xn+1n+1 +C∫dxx=ln x +C   The logarithmic…

Q: 2. Show that Re(iz)=-Im z. 3. Show that Re(iz)=-Im z.

A: