Suppose we have a set of three vectors S = {V₁, V2, V3} CR². Which one of the following is a true statement? (a) S will be a basis for R2 only if one of the vectors is the zero vector. (b) S will be a basis for R2 if and only if v₁, V2, and v3 are linearly independent. (c) S will be a basis for R2 as long as it is possible to write V3 = C1v1 + c2V2. (d) S cannot be a basis for R² because 3 vectors cannot span R². (e) S cannot be a basis for R2 because 3 vectors cannot be linearly independent in R².

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: Determine whether S = {(4,3,2), (0,3,2)(0,0,2)} is a basis for R³. If it is, write u = ( 8,3,8) as a…

A: We have to determined whether S=(4, 3, 2), (0, 3, 2), (0, 0, 2) is a basis for ℝ3 or not. also we…

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

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Q: The vectors -4 THELB 2 and V3 = -4 form a basis for R³ if and only if k +- VI 7 -6 0 V2 13 -14 k

A: The vectors v1=7-60, v2=-42-4,  and v3=13-14kform a basis for R3 if and only if k≠?.

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: For each of the linear combinations below, write the corresponding coordinate vectors. -4 1) Let B…

A: B contain vectors -4-1-4-1, 14-41, -1-4-4-1, -2-441v=1-4-1-4-1+-314-41+-3-1-4-4-1+1-2-441

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

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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: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: The vectors V, -5 [29] 24 [04.0₂ Write span R2 but do not form a basis. Find two different ways to…

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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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: Let ----0-- -2 = Show that {V₁, V2, V3} forms an orthogonal basis in R³. Express W= as a linear…

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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: Consider the polynomials p₁ (t)=3-t³, p₂ (t)=2-t², p₂ (t)=t-5t², and p₁ (t)=7-t+3t² −1³. 3 Is {P₁,…

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Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

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Q: Explain why S is not a basis for P₂. S = {1x, 1x², −1 − 5x + 6x²} OS is linearly dependent. OS does…

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Q: Are the following vectors a basis for P ? Explain why or why not. v = 1+ x? + x, = 1- x, vz = 1+ x +…

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Q: Find a basis B for the span of the given vectors. 8 HAD 0 1 8 -1 0 0 2 -2

A: We have to find the basis  B

Q: In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³…

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