1 4 Let S = {v,,v2,v,} where v, = -3 -7 %3D V2 = V3 1 1 3 1 3 a. Explain why the set S is not a basis for R ? b. Find the dimension of the span of the set S. c. Find the basis B for R that contains the vectors v and v2

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: Given the basis B if the coordinates of w relative to basis B are wR find w %3! 3 w = > Next…

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Q: 3. Let S= 2 and T be ordered basis for R'. Let v = 5 (a) Find the coordinate vectors of v with…

A: let S=111 , 023 , 02-1 and T=110, 1-10 , 001 be ordered basis for ℝ3 let v=35-2 (a) find the…

Q: If B={(1,1,1).(1,0,1),(0,1, 1) } is a basis of R3, then the second coordinate of the vector (3.5.7)…

A: On solving this we will get

Q: { be a basis for R? . Find the vector æ if [æ]R =| 3 Let B 8 x = x = 6. x = x = H 00

A: Given that B=11,21 be the basis for R2. We have to find vector x if xB=23. Since, xB=23 Hence,…

Q: (a) Find the coordinate vector of z = with respect to the ordered basis 4. E = 6. of R [æ]E = (h)Lot

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Q: Suppose v1, ..., V, are nonzero, mutually orthogonal vectors in R". a. Prove that they form a basis…

A: A set v1,v2,…,vn is a basis for a space V if every element in the space V can be written as a finite…

Q: 14. The set B = {1 – t²,t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

A: Given vector is: Pt=1+3t-6t2 Basis set for the vector is given as: B=1-t2, t-t2, 2-t+t2 Then, let…

Q: 4. In each case, check that {v1, ..., Vn} is a basis for R" and give the coordinates of the given…

A: According to our guideline, gave importance on student requirement solved subpart a and c. If you…

Q: The set S = is an ordered basis for R. If the coordinate 3. vector of a vector v with respect to S…

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Q: Given the basis B 1 5 if the coordinates of w relative to basis B are [w]B find w

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Q: Given the basis B = 18 if the coordinates of w relative to basis B are wR = -3 find w %3D W = > Next…

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Q: For what values of a do the vectors v, V2= V3= form a basis for R3? a O a++1 O a =+3 O a =+ 4 O all…

A: We know that a set of n vectors of length n is linearly independent if the matrix with these vectors…

Q: 7. Let S be the set S = a) Show that S spans R3 and find a basis for R3 contained in S. b) What are…

A: Given :  The given set is,   S = 1-20, 012, -568, 1-21  To find : (a) We have to show that  S spans…

Q: Given the following three vectors: Show that v1, v2, iz form a basis of R by proving that they are…

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Q: Find a basis for the set of all vectors in the form a + 2b + 3c 2а + 3b + 4с За + 4b + 5с [4а + 5b +…

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Q: Given the set of vectors determine whether the set of vectors is a basis for R

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Q: 11. For what value(s) of k does the following set of vectors form a basis for R³? ·4·0 3 3

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Q: Which of the following sets of vectors form basis for R3? Select one: 2 3 O b. None of these. 3 2…

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Q: Let ={t?-1, t²-t, -t?+t-2} be a basis for P,(R). Then the coordinates of p(t)=6t2-3t-1 are [p]= %3D

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Q: Given the following vectors, let W Span{v, v2, vs}. v3 (a) ( . Is z in W? Why or why not? (b) ( Find…

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Q: Do the following vectors form a basis for R? O a. Yes, the vectors form a basis for R2 O b. Cannot…

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

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: Question 2 Let B {V1, V2, ... , vn} be a basis for a vector space V and define vn+1 € V by Vn+1 =…

A: Step:-1 Part (i):- Basis of a vector space:- Let B= v1, v2, v3, ......, vr  be a set of vectors of a…

Q: The set B= {1-t,t-t,1- 2t-t} is a basis for P2. Find the coordinate vector of p(t) = 1+ 5t – 4t…

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Q: Let S V =R; S is a basis for V because Select one: O A. Gy tc,V, # 0 O B. The vectors are multiple…

A: s=11,-12V=IR2we need to show that s is a basis for Vfor this we need to show that the vectors11and…

Q: is a basis of then the second coordinate of the vector (3.5,7) in the basis B is: If B=((1,1,1),…

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Q: Which of the following sets of vectors is a basis for R?? {[:]}. 2 3.

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Q: The set B = {1+tť,-t+t,1-2t+t} is a basis for P2. Find the coordinate vector of p(t) =3- 3t + 8t…

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Q: Suppose S= {Pi;P2•P3;P4,P5;P6} is a basis for P5 and p is a polynomial of degree 4. Then the…

A: Given The coordinate vector is a vector in which each component is the coefficient of the linear…

Q: 1. Given the vectors u = (1,2,3); v = (3,6,7); w = (1,3,2) de R3 Verify that the set A = {u°, v, w°}…

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Q: Find a basis for S. a + 9b a - b , where a and b are real numbers. S is the set of vectors of the…

A: A basis for a vector space is a linearly independent set which spans the space.

Q: Which of the following sets of vectors is a basis for R?? {}E} 2

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Q: 3. Given the two ordered bases U, V below for R³ (also the standard basis E = [e1, €2, €3]) (): 1…

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Q: the vectors V = 9. a12 %3D -9 and 13/2 6. 3 form an basis for W, Find orthogonal or ther mal basis…

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Q: Given the ordered basis 9. B = { u1 1,u2 , U3 = 8 -3 22 find [v]B. the coordinates of v = -15 with…

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Q: Let v, V3= , and let H be the set of vectors in R° whose second and third entries are equal. Then…

A: The given is related to vector spaces. The solution is explained below.

Q: Let B = Note that B is a basis for R?. (You do not need to prove this. (a) Find the…

A: ANSWER :

Q: .2 The set B= {1 +t,-t-t,1+2t+t} is a basis for P,. Find the coordinate vector of p(t)= -3-5t-6t…

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Q: For the set of vectors S = {(1,2, –2), (0, 4, 2), (2, 1, – 1)}, show that S forms a basis in the…

A: Given: Set of vectors S = {(1,2,-2), (0,4,2), (2,1,-1)} To prove: S is a basis for R3 Concept Used:…

Q: 2) Let S contain vectors of the form Then a basis for S would be: a b : a-5b-6c = 0 and…

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Q: B = {3 – 3x, 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x…

A: We have to find the coordinate vector of P(x)=4+2x-6x2. w.r.t the basis…

Q: B = is a basis for R2. Find the coordinates of the vector x = relative to the basis B. -14 [x]B |

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Q: 4. Let S = {v1, V2, V3, V4, V5} where, 3 3 3 9 2 Ea 1 Sa 4 -3 -3 la 6 Find a basis for the space…

A: Here  v1 = 13-12,   v2 = 39-36, v3 = -121-2,  v4 = 21-20,v5 = 31-34The matrix is…

Q: Which of the following sets of vectors is a basis for R Select one: a. O b.

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Q: Consider the basis 3 3 6. B = 1 4 2 3 ,then v is the vector 3 of R. If [v]B =

A: Basis of a vector space is the linearly independent set which spans the vector space.

Q: Why is the given set of vectors not a basis for R^3? S={(1,2,-1),(1,1,1),(1,0,1)}

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Q: a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E…

A: as per the guidelines I am answering only first question (a) Let the coordinate vector of x=2-40…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.