The set B=(3+2x², 12+2x+8x²,- (29+6x+20x2)) is a basis for P2. Find the coordinates of p(x) = 8 + 4x + 6x2 relative to this basis: [p(x)]B=

Q: The set B= {2+z, 6+3z + 3z,- (23+9z + 12z*)} is a basis for P Find the coordinates of p(z) = - (73 +…

A: Coordinates

Q: Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1 + 4x + 6x², P2 3+x = (ii)…

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Q: In P2, find the the standard basis C = {1,t,t²}. Then find the B-coordinate vector for − 4 + 10t −…

A: We know that  is a vector space consisting of the set of all the polynomials of degree lessthan or…

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: Explain why S is not a basis for R2.S = {(−3, 2)}

A: We know the definition of basis, let V be a vector space. Let B be a set of vectors in vector space…

Q: , find the change-of-coordinates matrix from the basis B= {1– 2t +t?,3 - 5t + 41,2- 2t + 5t?} to the…

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Q: The first four Laguerre polynomials are 1, 1 –t,2 – 4t + t², and 6 – 18t + 9t² – t3. Show that these…

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

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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: Find a basis for the ideal √(x³ - 214 + 2x² - x, x5-14-21³ + 2x² + x − 1). ស

A: We have to find a basis for the ideal x5-2x4+2x2-x,x5-x4-2x3+2x2+x-1

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: Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

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: 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 a basis of the following linear system. { X1 2x1 x1 3x3 4x2 x2 + x3 + 2x2 + + 3x3 + 7x4 7x4…

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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: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

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Q: Consider the basis B = {{2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

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Q: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

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: 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: 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: -2 4 -21 A = -4 -1 -2 -2 1 A basis for the image of A is { }. To submit your answer, you may enter a…

A: Notice that :   In given matrix, (row 3) + (row 1) = (row 2) and row 1 and row 3 vectors are…

Q: please explain part d because i am confused by the second and third part of part d.

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

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Q: Let Pn = {anxn + an-1xn-1 + . .  + a1x + a0 | each ai is a realnumber}. Is it possible to have a…

A: The polynomial space is defined as follows: Pn=anxn+an-1xn-1+⋯+a1x+a0  |ai∈ℝ Check whether is it…

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

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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: moving targets. If the shooter is an arrowhead whose vertices at any point is in the span of row…

A: Given : A  =  413168101422Using elementary row operations R1  ↔  R2,  168413101422R2 - 4 R1,  R3  -…

Q: In P2, find the change-of-coordinates matrix from the basis B = {1-3t+1²,2-5t + 31²,3 - 6t+7t²} to…

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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: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

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Q: Extend {1 + x, 1 + x + x2} to a basis for P3.

A: Given set is ,                  1+x , 1+x+x2   (.)  Standard basis of  P3  is                    1 ,…

Q: In P,, find the change-of-coordinates matrix from the basis B = {1+3r²,2+t+7t?,1- 41} to the…

A: Given that                          B={1+3t2,2+t+7t2,1-4t} is a basis for ℙ2. To find the change of…

Q: -3x + 6y - z +t - 7v = 0 x - 2y + 2z + 3t - v = 0 2x - 4y +5z + 8t - 4v =0 Find the solution space…

A: Dimension = number of linearly independent vectors in basis.

Q: Let [1 -1 1 A = 0 -1 2 Find orthonormal bases of the kernel, row space, and image (column space) of…

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