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: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

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

A:

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 V be all elements of R2 that have the form (a, a2) where a is a real number. Show that (3,9) is…

A: Let V be all elements of R2 that have the form (a, a2) where a is a real number. We have show that…

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

A:

Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

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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…

A:

Q: 6. Show that there is a one-to-one correspondence between the Cartesian products A x B x C and A x…

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Q: Suppose J3 is derived from switching the rows of 13. -5 3 0 -8-1 7 -4 If AJ3 = 0 -2 7 -2 3 -5 -8 or…

A: NOTE: Refresh your page if you can't see any equations. . the 3×3 identity matrix is given by now…

Q: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

A: It is given that the addition is defined as x1, x2+y1, y2=x1+y2, x2+y1 and the multiplication is…

Q: why does z go from x2+y2 to 1?

A: Sketch the region E.