Given the operator S on the vector space R₁ [x] given by S (a+bx) = -a+b+ (at 2b) x A) What is SC1) written as a vector? B) What is S(x) written as a vector? C) What is Ms (B, B) in regards to the basis {1,x} ?

Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: With T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: The given matrix  and the vector  and  is defined by .The aim is to find the vector  whose image…

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Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

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Q: Let W be the set of all vectors of the form where a and b are real numbers. 2a+b (a) Determine…

A: Given, W=ab2a+b where a and b are real numbers.

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

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Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4v, - v,, 4v, +…

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Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (V2 - V, V1 + V2,…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, Vị + V2,…

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Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: Find the vector x determined by the given coordinate vector [x] B and the given basis B. 8) B =…

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Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

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A: Answer is 10.1

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Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: - 16] [1] Determine whether the vector v =| 17 |is spanned by the vectors and | 2 or not. 18

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Q: Consider A= (0, 4, 2), B =, (6,-1,0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

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Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

A: We know that the dimension of vector space  is 3.If the given three vectors are linearly…