Consider the following ordered basis for P₂ (R): B = {x² + 2x + 1, x + 1, 1} (a) The quadratic polynomial that has [[1], [3], [2]] as its coordinate vector relative to B is: (b) The coordinate vector (relative to B) of x² + x + 1 is:

Q: (3) For each of the following sets, determine whether it is linearly independent or dependent. (a)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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A: In this problem ,we use the concepts of linear combination.

Q: Let f(x) = −4, g(x) = -5x+7 and h(x) = - -2x29x+9. Consider the inner product (p,q) = p(-1)g(-1) +…

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Q: (a) Calculate the resultant of A = 3x² +3 and B = (x-2)(x+5) by hand. (b) Let A, B, C be…

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A: That's easy. Have a good day!!!

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A: Solution attached in detail in step 2.

Q: Exercise 9.2.6 For each of the following sets of polynomials, determine whether the set is linearly…

A: The set  is linearly indepemndent if Otherwise linearly dependent.

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

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Q: Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||pl|, |la||, and d(p, q) for the…

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Q: {x²+x, -2x² - 4x-6, 2x-2}.

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A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) +…

A: Step 1:Step 2: Step 3: Step 4:

Q: 2d

A: Definition of P2​(R): Space of polynomials of degree at most 2 with real coefficients.Introduction…