Show that P2(R) can be spanned by P1, P2 and any polynomial po(t) = c, where cЄR, and c = 0. (2) Consider the space P2(R) of all polynomials of degree at most 2, equipped with the standard polynomial addition and scalar multiplication.

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A: Given matrix

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A: Average rate of change = 1 Explanation: Given that, f(x)=3x2−2x+1 we have to find the average rate…

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A: Option D is the correct optionExplanation:Step 1:Step 2:

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A:

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A:

Q: 12. Consider the linear regression problem: y (m) = lo + Br2m) + ... Bo + B1x + Bpx (m) + € (m), m =…

A: proof is given below in the explanation corner.Explanation:

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A: To calculate the total capital gain for Question 1, we'll use the formula:\[ \text{Total capital…

Q: Use the difference of two squares to find the product of 22 and 18. Complete the steps. = 396 +…

A: (20 + 2)(20 - 2) (20)2 - (2)2 =396Explanation:

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Q: (3 marks) Let r Є R and u = v ■- (2) - (+) w- () (+), -4 " W = For which values r = R is the set {u,…

A: The vectors are linearly independent for all r except 1. Explanation:

Q: Make the indicated conversions. (a) 7 m = km. (b) 7 mL: = dL (c) 7 mL = L (d) 7 mL = KL

A:

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A: The simple interest formula Amount at time tInitial amount Rate of interest Time in years

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A: To solve for the matrix  if .Assume that all matrices are  and invertible as needed.

Q: Which of the following regulations defines the associative binary operation ° on the set R^n×n…

A: Which of the following regulations defines the associative binary operation ° on the set R^n×n…

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A: In decimal: f(t)=9e−0.0715t Or    We can also write: f(t)=9eln(0.931)tExplanation:

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A: The correct answer is 3.Explanation:Detailed explanation:Let's break down the truth table and the…

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A:

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A:

Q: oblem 8. Prove that if u is an eigenvector of A, then u is an eigenvector of A² as well.

A:

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Q: Question 10. Solve and show work. Thanks.

A: B=⎣⎢⎡​3/20−17/209/20​321​1263​⎦⎥⎤​Explanation:Given,A=⎣⎢⎡​01−1​312​303​⎦⎥⎤​Given condition,AB=A+2BWe…

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A:

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A: Graph is attached and region is shaded.Explanation:

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A:

Q: O Week 2: Systems of Linear Equations Graphing a linear inequality in the plane: Slope-intercept…

A: Please find the attachment for the graph.Explanation:

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A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Question 8. Show work and solve, thanks.

A: Please refer below page.If you have any questions feel free to ask.Explanation:

Q: Complete the description of the piecewise function graphed below. Use interval notation to indicate…

A: f(x)=⎩⎪⎨⎪⎧​4 if x∈[−5,−2]−4 if x∈(−2,1]−1 if x∈(1,4]​Explanation:In a graph, open and closed…

Q: Write a value in each region that makes the inequality or inequalities true. -4(x-2)≤0 -12-2(8-x)

A: To write a value in each region that makes the inequality or inequalities true.

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A: Given We have to find

Q: 2 -6] The matrix -5 k is invertible if and only if k + #☐

A: Given Matrix is as follows

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Q: Plz help Don't use chat gpt

A: