3. Show that if (AB)₁, (αB)₁, (Aß)₁, (αß)., and (AB)2, (αB)2, (AB)2, (aß)2, be two aggregates corresponding to the same value of (A), (B), (α), (ß), then (AB)₁ - (AB)₂ = (aB)₂ - (αB)₁ = (AB)₂ - (AB)₁ = (aß)₁ - (αß)₂

Q: 1. Let A = {a, h, g}, and B = {3,6}. Answer each of the following questions. %3D (а) Ах В (b) В х В

A:

Q: 2. Let L1 bg 3D (-1,2, 1,3, 3), сі %3D (3, —4, 0, — 4, 3), сэ %3D Find a basis of Lin L2 and L1+ L2.…

A:

Q: let u=(1,2,3), v=(3,2,1) and w=(4,5,6) u.(2v)= Select one: 1/20 20 -20 -1/20

A: The given vectors are: u=(1, 2, 3)v=(3, 2, 1)w=(4, 5, 6)

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: If 7 - 2 1 8. [1 -2 -2 -4 A =|- 2 3 B = -1 -3 , C =| 0 3 and D= 1 - 4 - 7 [2 - 4 | then find (A' –B'…

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Q: In (IR, 7sorg), if A = T. sorg :n EN and B = (2, 3) then AUB=

A: A closure is the smallest closed set containing A.

Q: a=(3,2,-1), b=(1,-1,2),

A: Given: a=3, 2, -1 and b=1, -1, 2 To find:  1. a×b 2. a+2b×b 3. a·3b 4. b×a·c 5. b×3a-2b

Q: 4- Suppose that A = {x1 = (2,0,1), x2 = (1,–1,4), x3 = (-1,–2,1)} and B = {y, = (-1,0,2), y2 %3D %3D…

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Q: (2 3. Let A = G) and B = (; ). Compute and compare: %3D a. Det(A + B), det(A) + det(B). b. det(3A),3…

A: We have A=2-135 and B=1211 Part(a) Now if we have a matrix M=abcd, then, detM=abcd=ad-bc Therefore,…

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

A:

Q: Every combination of v = ( 1 , -2, 1 ) and w = ( 0, 1 , -1 has components that add  to __ . Find c…

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Q: Find the difference between the sum of the first 11 terms of {an} and the sum of the first 11 terms…

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Q: Let R = {(3,4),(1,3),(4,2),(4,1)}, Then R² is given by O (1,3),(2,1),(3,2),(4,3)} O {(1,3).(2,1).(3,…

A:

Q: AN 3. Given R(x) = a) R (-1 3x-1 TED COMPILED ANDEDIB COMPILED AND EDITE COMPILED AND SoCOMPILED AND…

A: This is a composition of functions.

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

A:

Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: a communication source emitting the following symbols S = {a, a2,a3}. Find P(a,) if 1. P(a,) = and…

A:

Q: and y= If a = 3, then x =

A: Solve using the properties of trigonometric rations

Q: Express the following as linear combinations of 1= (2, 1, 4), v= (1, – 1, 3), and w= (3, 2, 5). 8.…

A:

Q: 18

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Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

A:

Q: Suppose v4 = 20 – 02 + 503. Let w = 601 + 202 – 303 – 204. (a) Write w as a linear combination of…

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Q: 5. Let a = = (2 5 9) o (1 3 6) and 3 = (1 5 7) 0 (2 4 6 9) € Sg. Find ao Boa-¹.

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Q: 5. If Ā= 2 4 If A and B -2 3) find: 5 7 (a) AB (b) Ã+E (c) 2A" - E (d) a" (A- E)

A:

Q: 7. (S.15). Find the inverse A-1 of the matrix -2 -3 A = 0 2 -1 -1 -2 3

A: Matrix Question

Q: (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b;…

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Q: 4. Find z, and z, such that, 2iz, +iz, 2+5i and = 9-11i 3i z,-2i 2, 4 =i+1, z, = 3+4i (b) z, = 3-4i,…

A: Solution:- let z1 and z2 be the different ccmplex number i2= -1 i3=-i

Q: Suppose a, = (1 -1 1 1) 5. a, = (1 0 1 0)" a, = (1 1 1 1)'a, = (3 2 3 0)" · Please find out whether…

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Q: Let 1 1 0 1 a b A= 12 B= 20 C=|c d . If C = A + 2B, then a. a = 2, b = 1, c = 5, d = 3. b. a = 3, b…

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Q: 3. Consider A={m,a,t,h}; C={x:x=3n,1sns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n S6,nEN} What is ANB?

A:

Q: Show mathematically that (10-6) is not independent of (10-1),(10-3), and (10-4).

A: We can write (10  -6) as:

Q: 11. The first row of AB is a linear combination of all the rows of B. What are the coefficients in…

A: We have to find the ist row of AB

Q: The height of adult males from a specific species is normally distributed with an unknown mean a and…

A: Claim : the true population mean height u is more than 2 meters.

Q: a) Let A and B be two regular (nonsingular) (n, n)-matrices. Determine whether the following is…

A:

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

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Q: カーて A %3D 3.

A:

Q: əz and əx əz 9. If x²y + y²z + z²x = 10 , where x and y are independent, determine ду -x2-2yz az…

A:

Q: 9. Given u =(2,-2), v = (5,8), and w = (-4, 3), find each of the following. (a) u v (b) (u - v)w (c)…

A: