Instead of using the standard definitions of addition and scalar multiplication in R³, suppose these two operations are defined as follows. (x1, Y1, 21) + (x2, Y2, 2) = (x1 + x2 + 1, y1 + Y2 + 1, z1 + 22 + 1) c(x, y, z) = (cx + c – 1, cy + c – 1, cz +c – 1) With these new definitions, Show that it satisfies the Axioms 5,6, and 7

Q: W laLer Prove the polynomial identity below: (2 – 4y² )² + (4zy)² = (z² + 4y)

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Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

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Q: X1 3x2 + 5x3 + 15x4 T(x) = |3x₁ + 8x2 − 2x3 − 23x4 4x17x2 + x3 - 16x4

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

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Q: Determine the product of the following: (x - 3) (x + 7) O x2 – 4x + 21 |- O x? + 4x – 21 O x - 10x +…

A: The given equation is:    (x-3)(x+7)

Q: Write the following complex polynomials in factored form. You may check your final answer using…

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Q: (c) How many of the elements of Z186 have multiplicative inverses?

A: To find the number of elements in the set of integers modulo 186, which have multiplicative inverse.

Q: I have performed the following polynomial multiplication in matlab on two vectors of polynomial…

A: Since matlab is mymult=conv(v1, v2) and result is mymult=3 45 -6 -78 99 65 -54 -12 -10 240

Q: (d) Show that x² + x +4 is irreducible over Z11. (e) Write x³ + x² + x +1 as a product of irrducible…

A: An irreducible polynomial is a non-constant polynomial over a field that cannot be factored into the…

Q: 2 + v - , 2+z+ 11. 0. di

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