Prove that the equation ax + b = c where a, b, c constants and a 0 has a unique solution.

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Q: x1 + 5х2 + 3x3 4x1 + 2x2 + 5х3 2х, + 4x2 2х1 - = 14 3 16 3x3 + 8x4 + 6x5 = 2х5 X3 = 0 0

A: x1+5x2+3x3                               =144x1+2x2+5x3                            =3…

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Q: Given the vectors OA.O v₁=(-1,0,2), v₂= (0,2,-3) and v₂=(2,2,3), suppose v is another vector which…

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Q: Find the inverse of 1 + √2 in Z[√2]. What is the multiplicativeorder of 1 + √2?

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A: Given :  x1+2x2-x3+x4=22x1+x2+x3-x4=3x1+2x2-3x3+2x4=2 To Find : (a) Solution of given system…

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Q: 5) Use long division to find the quotient Q(x) and remainder R(x). P(x) = 6x³ 2x² + 4x - 1 and d(x)…

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A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

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Q: 8. Suppose a, b e Z. Prove that a = b (mod 10) if and only if a = b (mod 2) and a = b (mod 5).

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Q: 5. Let U = {(u₁, U2, U3) E R³|u₁ + u2 - u3 = 0} and V = {(V1, V2, V3) E R³v₁ - 3v2 +5v3 = 0}. (a)…

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Q: Write down the negation of the following statement: Every duck has at least three white feathers.

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Q: Draw a valid conclusion from the given premises. If a guitarist strums an E chord, then they're…

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