Consider the set H := {a + bi + cj + dk | a; b; c; d element of  R} such that (i) i2 = j2 = k2 = -1, (ii) ij = k; ji = -k; jk = i; kj = -i; ki = j; ik = -j; (iii) every a element of R commutes with i; j; k. (a) Let q = a+bi+cj+dk and w = e+fi+gj+hk be two arbitrary elements of H. Write the product qw in the form z0 + z1i + z2j + z3k, where z1; z2; z3; z4 2 R. (b) Find A element of R4x4 and b element of R4 (both related to q and/or w) such that Ab =  z1 z2 z3 z4

Q: conjugate of v-1-3 is 1- V-1+3 2- -V-1-3 -V-1+ 3 3 - V-1 2- 4-

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A: The solution is given as

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Q: LetP(A) = 0.10, P(B) = 0.20, and P(A∩B) = 0.02. Are A and B mutually exclusive? Justify your result…

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Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

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Q: d) Prove (AV (Vx) BC = (Vx)B(AV C), as long as x not free in A. (Hint: Translate first to Standard…

A: Given,  Prove (AV (Vx)BC = (Vx)b(A V C), as long as x not free in A. (Hint: Translate first…

Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: Q1: Sketch the signals A. x(t) x(-1/2) A CL x(2(1+2)) x(−1+1) Ates Ades 0 2 B. 2 x(t) 0 1 x (3t),…

A: Given data:- Part A=   Part B

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A: Find all non-negative integer pairs of (x, y) such that .

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

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Q: Let a=⟨−3,−2,2⟩ and b=⟨−4,−2,0⟩ Compute:

A: Given that          a = <-3, -2, 2 >    and    b = <-4, -2, 0> Here we have to compute…

Q: Let (4A)−¹= 2 4 -3 2 Get At.

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A: Given: A is row or column consisting entirely of zeros .

Q: Suppose ū=i- j, v = −2i + 4j+3k and w = -5i + 4j. Compute the following values: |u| + |v|=| |-6u|…

A: Since you have posted a multi subparts question according to guidelines I will solve first(1,2,3)…

Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

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Q: Find the string that has this generating function: a) (1− x)−3 b) (1+2x)−4 c) 1/(1 −3x)3

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Q: 2j(5-j3) B) Given that (2a+jb)+(b-j3a)=- Obtain the values of a and b. (2+j)(1+j4)

A: Solve the left and right-hand side independently left-hand side 2ab+3ab+jb2-6a2 5ab+jb2-6a2…

Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). – 2,0). - - 2u + 20

A: Given:-u→=<3, -4, -10> andv→=<-7, -2,  0>

Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

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Q: Let f = {(1,-1), (4,-2), (9,-3), (16,4)} and g = {(-1,-2), (-2, -4), (-3,-6), (4,8)}. Show that gof…

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Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Determne whether the hamit exitis or not when a)x3 and b) x→ -3 x²-9 when x< -3 F(x)= 9-x² when -3<…

A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: Given u = 21+j-6k and v = i-4j+ 3k, find (u•v)v. O (u•v)v =-20i+ 80j–60k O (u•v)v=-40i–20j + 120k O…

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Q: LetP(A) = 0.20, P(B) = 0.80, andP(A∩B) = 0.16. Are A and B independent? Justify your result…

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Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

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Q: Am = 7+ m Bm 2 min {5-m(-1)m+3, 7} R= {m EN: Bm = -4m}, V = {m EN: Bm = -8}, W = {m EN: Bm = 1}. max…

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