Let 0 = V5 and K = Q(0). Two bases for K over Q are a = {1+0,1+ 0²,1+ 0³, 1 + 0ª} and B = 1+ 0² 0+0³\ , 0, Evaluate the discriminant of the a basis and the discriminant of the B basis. Compare to D(0).

Q: Find a basis B for the span of the given vectors. B = [01-41] [51-10] [4191] 11

A: Basis for the span of the set of vectors: To find a basis for the span of a set of vectors, write…

Q: Write down a basis of R 4 where you don't use any of the standard unit vectors (e1, ... , e4). Show…

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Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Let B = 3 (1, x + 8, (x − 1)², 2x³) be an ordered basis for P3. Find the coordinate vector of 3 -…

A: fB​=[161, −19, −6, 4]Explanation:Detailed explanation:This is a detailed guide explaining how to…

Q: The set B={1-1², -2t-t², 1-t-t²} is a basis for P₂. Find the coordinate vector of p(t)= -3-11t-2t²…

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Q: Find the 2 x 2 matrix P such that Pu is the orthogonal projection of in R² onto the line consisting…

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Q: } 4. You are given that B = {1– 2x + x?, x+ x?, 2 +x – a?} is a basis for P2. (i) Find the…

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Q: Let B = (1, x + 7, (x − 1)², 6׳) be an ordered basis for P3. Find the coordinate vector of f(x) =…

A: Given,                be an ordered basis for  and             To find the coordinate vector of…

Q: The set B is a basis for R². Find the coordinates of the vector [Z] B 9. -10] relative to the basis…

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Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: (1 point) The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are…

A: Solution:

Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: https://www.youtube.com/watch?v=pE5yxgmXMmQ&t=267s This video was given as a guide

A: ANSWER AND SOLUTION: To find the coordinate vector of the polynomial f(x) = −8x3 + 3x2 − 3x + 7…

Q: Let B = (1, t + 8, (t – 1)², 4t° ) be an ordered basis for P3. Find the coordinate vector of P(t) =…

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Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

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Q: Let B, D be the following two bases of R³: -1 B = D= a) Find the change of coordinates matrix Po-s…

A: Solution is below.

Q: 1. Show that the vectors (1, 1,0), (1, 1, 1) and (1,0, 0) are a basis of R3. Find the coefficients…

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Q: Q. If B = {e, = the usual basis R2. Determine its dual basis. ?? ده رده را( = (D, 1)} is

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Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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

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Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: 5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1),…

A: we will find the coordinate vector with respect to the given basis.

Q: If B= {(1,1,0), (0,1,1), (−1,0,2)} is a basis of R³, then the coordinate vector of v= (8, -5, 3) in…

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Q: Matrix A is factored in the form PDP'. Use the Diagonalization Theorem to find the eigenvalues of A…

A: Given: A=20-2234003=-20-1012100300030002001214-10-2 Since A is diagonalizable , P is an invertible…

Q: 6. Let B be the following ordered basis for R?: в %3 {(1,—1), (2, -3)} . Find the coordinate vector…

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Q: If B = {(1,1,0), (0,1,1), (-1,0,2)} is a basis of R³, then the coordinate vector of v = (2,0,1) in…

A: Solve the following

Q: The vectors : 1 3 5 2 = = 11 --8-8-6 = 0 7 form a basis for R³ if and only if k k

A: Given vectors form basis for R^3 iff when k=21.Explanation:Three vectors from R3 from basis for  R3…

Q: Let TilPe P. Tlax²+ bx+c) = 20x+ b. Then the basis of NIT) is O True O False

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