The set B = {4+x², 20 - 3x+5x2, 45-6x + 11x2} is a basis for P2. Find the coordinates of p(x) = 6x - 33 - 8x2 relative to this basis: [p(x)]B=

Q: B = [3 {[9][9]} 02 4 0 56

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

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Q: Given 4 1 -3 -1 2 A = 3 4 -6 8 0 -1 3 Find a basis of the row space of A.

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Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

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Q: Given basis = {QOB]} {[ 2 5 3 {C₁, C2, C3}. find the basis C = of R³ and change of basis matrix [B]C…

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Q: Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for…

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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: 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: Show that A is diagonalizable.

A: Consider a square matrix A. Then A is diagonalizable if there exists an invertible matrix P such…

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: Find a basis for the space of 2 × 2 lower triangular matrices. Basis = {[ 9. 9.

A: Basis = {[10​00​],[01​00​],[00​01​]}​Explanation:ANSWER :​​

Q: Find the change of basis matrix [B]. {0}{000) C = B = -2 -3 2 -2 -31 2 4 5 -3

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Q: 1. Decide if p lies in the span of {v1, v2, v3}. If it does, find a linear combination that makes…

A: We determine if p(x) = x - x3  lies in the span of the vectors v1(x) = x2, v2(x) = 2x + x2, and…

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

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Q: Find a basis for the solution space of the given homogeneous linear system. Xy - 3x2 + 3xy - 3x4 = 0…

A: The homogeneous linear system is x1-3x2+3x3-3x4=02x1-5x2+12x3-4x4=0The corresponding matrix form…

Q: c. If a matrix has more columns than rows, then the dimension of the column space is bigger than the…

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} O S is linearly dependent. O…

A: Consider the given functions. S=1-x,1-x2,-1-4x+5x2 Let S is linearly independent and there exist…

Q: (a) Find A-1. (b) Use answer from (a) to solve Ax = b. (c) Use answer from (b) to express b as a…

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Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

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