(5) The ring (Z6, +6,•6 ) has that rad Z, (a) ((0), +6.-6 )

Q: 2 Consider the bases B₁ and B₂. 2 -3 -7 4 {{³][])} {₁ 6 -5 B₁ = Find [x]B₂ if [x]B₁ 2 [²]. 6

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Q: Let A be 4x4 and det(A)=3. Then det(24)=. and det (A" A)=.

A: Given A be a 4×4 matrix and detA=3

Q: Find the coefficient of z in -5 "Co-"C +"C2 +(-1)" 27

A: Consider the given binomial expansion: C0n-C1n2x-1x+C2n2x-1x2-.......+-1n2x-1xn Here, the objective…

Q: 3 Let x = (9, −9, −4) and y = (-6, 6, -9) be in R³ and a be in R. Then ax + y = ( ,23).

A:

Q: verify that 6A = 3(2A)

A: Here given  Thus

Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

A:

Q: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

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Q: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

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Q: Show that (z3 z4) -1 = (z3-1. z4-1)

A: We prove the given statement by taking Z3=x3+iy3, and Z4=x4+iy4. After using the fact of…

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

A:

Q: n the ring Z5 × Z7, determine −(3, 6) and (3, 6)−1 .

A: Here given ring is R = Z5 × Z7  We know that properties of ring R  If (a,b) is element of R then, i)…

Q: What are the zeros

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Q: The product of x* + x3 + 2x? and 2x² + 4x + 6 in z, [x]/ is:

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Q: (5) The ring (Z6,+6,•6) has that rad Z, = (a) ((0), +6. -6 ) (b) ((2), +6.•6 ) (c) (3), +6,-6 ) (d)…

A: Definition: A radical of a ring R is defined as the intersection of all maximal ideals in R. Given:…

Q: If y = (5x + 1)(2x¯1 – In 7), then y' will be (5x + 1) (금+)+ 5(2x1-In 7) A. B. (5x + 1) (--) + 5(2xt…

A:

Q: Q3) Use the inner product = a,bo + a,b1 + azb2 to find , llp||, d (p, q), and then find the angle…

A: Given: Inner product: p, q=a0b0+a1b1+a2b2 and the polynomials  p(x)=1-x+x2 and q(x)=x-3x2. To find:…

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

A:

Q: a) Variable Separable/Homogeneous Equation (x − y ln y + y ln x)dx + x(ln y − ln x)dy = 0

A: As per our guidelines, we can answer only first question and rest can be reposted. Using variable…

Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

A:

Q: If 8 = (AB)–- (AB), then with usual notation, prove that %3D (i) [(A)- (a)] [(B)- (B)] + 2 N 8 (AB}…

A: ANSWER: For the given data,