The set B = {2 + x², 6 + x + 3x?, 19 + 2x + 9x²} is a basis for P2. Find the coordinates of p(x) (39 + 2x + 18x* = - relative to this basis: [p(x)]B

Q: The set B = {2 - 2x², 6 - 2x − 6x², 13 - 6x - 12x²} is a basis for P₂. coordinates of p(x) = 18x −…

A:

Q: The set B = {3+4x², 12 − 3x + 16x², 9x - 25 - 36x²} is a basis for P₂. Find the coordinates of p(x)…

A: Here we have to find the coordinates of p(x) relative to the basis B.

Q: The set - B = {−2+2x², −6+ 4x + 6x², − 6 + 8x + 8x²} is a basis for P3. Find the coordinates of p(x)…

A: Given basis is .Also given that we have to write down it as linear combination of basis elements,Now…

Q: The set B = {4x²3, 12x² (9+x), 38+ 3x - 48x²} is a basis for P₂. Find the coordinates of p(x) = 44+…

A: Given; B=(4x2-3, 12x2-(9+x), 38+3x-48x2) p(x)=44+3x-56x2

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: The set B = {4+x², 20 - 3x+5x2, 45-6x + 11x2} is a basis for P2. Find the coordinates of p(x) = 6x -…

A: 30-1Explanation:

Q: The set B = {4 — 4x², 12 - x - 12x², 33- 3x - 32x² } is a basis for P₂. Find the coordinates of p(x)…

A:

Q: {(:}) (::). (; })· (; )} 1 1 1 2 2 3 3 4 2 2 3 4 5 1 7 3

A:

Q: Let P² be the vector space of all polynomials with real coefficients of degree at most 2, with the…

A:

Q: :) The set B = {-(1 + x²), 3x − 4 − 4x², 7 - 6x + 6x²} is a basis for P₂. Find the coordinates of…

A: Let us consider the element v and B be the basis then,  To write the vector v in the linear…

Q: basis: The set B = {4x² – 3, 16x² − (12 + x), 28 + 2x − 36x²} is a basis for P₂. Find the…

A: Answer  Given p(x)=108+9x-140x2 and B={4x2-3,16x2-12-x,28+2x-36x2}

Q: Question 2. Are the polynomials x2 – 2x + 1, 2x2 – 3x – 6, -x² + 5x – 3, Зд2 + 8х — 6Е P2: b) a…

A:

Q: Determine whether the set {x2 + 2x - 3, 2x2 + x - 1, 3x2 + 2x - 2} is a basis for P, by solving the…

A:

Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

Q: Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the…

A:

Q: Consider the polynomials p₁ (t)=3-t³, p₂ (t)=2-t², p₂ (t)=t-5t², and p₁ (t)=7-t+3t² −1³. 3 Is {P₁,…

A:

Q: Extend {l + x, 1 + x + x2} to a basis for P 2.

A:

Q: Consider the basis B3 = (x² - 1, x, 1) of P2 (R). Find [2x² + 3x − 5] B (2,3,-5) (2,3,-3) (3,2,-5)…

A:

Q: Let [3³] Ai B , where B = {b₁,b₂} is a basis in R². Then 3 B 061+06₂

A:

Q: Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to…

A: Solution is in explanatio area.Explanation:

Q: Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to…

A:

Q: The set B = {− (1+3x²), − (2+2x+6x²), − (6+4x+21x²)} is a basis for P2. Find the coordinates of p(x)…

A:

Q: ?:R3 →R2,with? ?,?,? =(?+2?+3?,4?+?−2?) Find a basis for the image and state its dimension.

A:

Q: The set B = {3 − 3x², 15+ 4x − 15x², 48x² - (47+ 12x)} - - is a basis for P2. p(x) = 12x² [p(x)] B…

A:

Q: basis: The set B = {-(4+x²), x − 12 − 3x², 49 − 3x + 12x²} is a basis for P2. Find the coordinates…

A: Let the coordinates of p(x) = 4x - 40 - 10x2 w.r.t the given basis B be (a, b, c)t  Then,      4x -…

Q: The set B={3-2x², 9+x-6x², 24x² - (34+ 3x)} is a basis for P₂. Find the coordinates of p(x) = 90x² -…

A:

Q: The set B = {2+ 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x) =…

A: Given Basis: B=2+2x2, 4-3x+4x2, 19-9x+18x2. To find: Find the coordinate of px=84-39x+80x2 relative…

Q: Is the following a basis for R3? Justify your answer. 0 3 2 1 -5 2 1 2 -3

A: Result:(i) If a subset S of  forms a basis of . Then S is linearly independent.(ii) If a subset S of…

Q: Use the standard basis for P2, B = {1, t, t²}, and the coordinate mapping to show that 10 – 12t –…

A: The solution is below.

Q: The set B = {4- 2x², 12 + 3x − 6x², 18x² - (35 + 6x)} is a basis for P₂. Find the coordinates of…

A:

Q: B = {3 – 3x, 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x…

A: We have to find the coordinate vector of P(x)=4+2x-6x2. w.r.t the basis…

Q: The set B = {2 + 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x)…

A:

Q: Write a basis for the Image of the transformation associated to {:}{: x + 4y 2x+8y y The first…

A: The given linear transformation,.The aim is to find the basis of the image of the transformation.