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: The number of integer values of m, for which the x-co- ordinate of the point of intersection of the…

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Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

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

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Q: The (i.j)-entry of (AB)' is the (j,i)-entry of AB, which is Oa1;b1j + a2;b2; + + anibnj .... O…

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Q: Let p = 5x + 10x + 3. Find the coordinate vector of p relative to the following basis for P2, P1 =…

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Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

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

Q: Let u = 2i+j-k and w=-3i+4j+k. Find uxw Select one: O 5i-3j- 11k O 5i+ 13j+ 11k O 5i+j+ 11k O None…

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Q: -1 -2 -3 -41 1 2 3 Let A = 1 2.) Find adj (A)

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Q: Calculate Vv and V x v. a) OV-v=-2x²yz and V × v = 0 b) OV v = 2yz + 3 and V x v = -2xi+ 2xyj +…

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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: If A has a row or column consisting entirely of zeros, then Select one: a. A is nonsingular b. A is…

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

Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

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Q: Find d = gcd (270, 105) and hence find integers x , y such that d = 270x +105y .

A: GCD stands for greatest common divisor for two or more numbers.

Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x<0xx≥0. If we take x=-2, then f-2=2…

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…

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Q: The set of polynomials {3t²-3t+5, mt+6t²+10} is a linearly dependent set in P, if 2 m=6 Select one:…

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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: 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: b) Find 4°f(x) if f(x) = (3x+1)(3x+4)(3x+7) ... (3x + 19) %3D

A: We will answer the first question only as we don't answer multiple question at a time. Please…

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: The first-order logic formula vx A(x)^3y -A(y) is satisfiable but not valid

A: Given that a first order logic formula ∀x A(x)∧ ∃ y¬A(y). We need to check that is it valid,…

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: The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A…

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Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

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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.