2. Find all values of k = R (if any) such that k 個 {1}· [4]} s k is a basis of R².

Q: 2. Let z -1 + i √2 (i) Determine the modulus and the Argument of z. (ii) Locate z, 2², 2³, 24, 25,…

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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: Let T: R* → P2 be defined as T | | = (a + b)t² + (c – d)t + d. a. Find T b. Find a basis for the…

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Q: If Pn is the space of polynomials of degree at most n with a basis B = {1, x, x², ..., xª}, compute…

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Q: (a) Write the equation in slope-intercept form, and determine the slope and y-intercept. (b) Graph…

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Q: Let A = 12 14 3 1 0 1 02-30 1000 Find a basis for the column space of A.

A: As per the question we are given a matrix and we have to find a basis for the column space of

Q: b. Prove that the polynomials p₁(t)=1, p₂(t)=1-t, and p₂ (t)=1+t-t², form a basis for P₂.

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Q: A shopper buys cat food in bags of 3 lbs. Her cat eats 3434 lb each week. How many weeks does one…

A: Given that A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week

Q: 3. Find a basis for the vector space RX] of all polynomials in X having degree at most 4 such that…

A: We have to find a basis for the vector space R4[x] of all polynomials in X having degree atmost 4…

Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

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Q: 1. Let B₁ = = {-1} {[]} i) Find Rep ii) Find Rep B1 and -{[]} B2 = be two ordered bases for R² C…

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Q: *) Let P₂ be the vector space of polynomials of degree 2 or less. Consider the following two ordered…

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Q: 4. Let A = [1 1 1]. Find a basis of N(A) and C(A).

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

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Q: 5. Determine whether S is a basis for P2 . хоо Oltx2 0 S = { x, 1 + x², x-x²}

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Q: Suppose that you have $11,000 in a rather risky investment recommended by your financial advisor.…

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Q: (a) (b) (c) Let W be the subpace of M2x2 (R) b W = { [20 + $ 30+d]:akedER} a, b, c, Find a basis for…

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Q: Let B = {1+x, 1 – x², x + 2x²} and p(x) = 7+ 10x + 11x². You are given that B is a basis for IP2.…

A: NOTE: Refresh your page if you can't see any equations. . write all polynomial as a vector

Q: 3. Let P2(R) be a vector space (over the field of real numbers) of polynomials p (t) of the degree…

A: We can give the example standard basis one And to check the basis we have to check the linearity…

Q: The set C = {1+ t²,t +t², 1+ 2t + t²} is a basis of P2. Find a vector q e P2 such that [q]c

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Q: Let B = {1,1+x,1+ x + x² }. (a) Check whether that the set B is a basis for P2. 2 (b) Let p(x) =…

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

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

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Q: Define T:R2 R2 by T(x) = Ax. Find a basis B for R2 with the property that [T] is diagonal. A = 51 15…

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Q: Quest In P₂, let B and C be the bases where B = {1-312, 2+t-5t2, 1+2t) and the standard basis C =…

A: I have given the answer in the next step. Hope you understand that

Q: 2: Consider B= a) Show that B is a basis for R³.

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