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

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: 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: Given the ordered basis B - {m = ["] = {u1 , U2 find [v]g. the coordinates of v = with respect to B.…

A: Let β= u1 , u2 , ...... , un    be an ordered basis for a finite dimensional vector space V. For x ∈…

Q: 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…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Given the ordered basis B = {ui U2 = 13 with respect to B. -12 find [v]B, the coordinates of v = Ex:…

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Q: Given the ordered basis 1 B = -1 3 , U3 u2 8 -14 find vB, the coordinates of v = -21 with respect to…

A: Since B is the basis of vector space. So there must exist scalers α,β,γ from field such that  Vector…

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: The coordinates of v relative to the basis C are given by [v]c = P[v]g. C-B" [v]c = P[v]s C+B -72

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Q: The set {GG} B = -12 is a basis for R?. Find the coordinates of the vector i relative to the basis…

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

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Q: Let V=R? and let (R?)* be the dual space for R². Subtask (a). Find the basis {d1, þ2} that is dual…

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Q: Which of the following sets of vectors is a basis for R´ Select one: а. b. c. d.

A: The basis of vector space can be determined by the number of independent vectors. If the number of…

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: Let V = P2(R). Show that 3 = {1+r+2²,x+r², x²} is a basis for V. [You may assume that we already…

A: We will use the fact that if DimV =3, then any subset of P2(R) consisting of three linearly…

Q: 1 2 1 1 1 with respect to the basis B = of M22" Find the coordinate vector of A = 3 4 [A]g =

A: Let V be a vector space and B=v1,v2,....vn be the basis of the vector space. Now, any vector in the…

Q: (e) Explain that Sį is a basis for R3 and that S2 is not. (f) Determine the coordinates of X1 U =…

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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: Define T: R2R? by T(x)= Ax. Find a basis B for R with the property that [T]g is diagonal. 2 -5 A =…

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Q: Given the ordered basis B = {p1 = 9 + 2æ, p2 = -4 – x}, find [p]B, the coordinates of p = -39 – 9x…

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Q: 18 Given the basis B -2 1 7 7 if the coordinates of w relative to basis B are wB - 4 find w 2

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Q: Given the ordered basis B , U2 5 find (v]B, the coordinates of v : with respect to B. Ex: 5 (v]s

A: Given: and Notice that v=u1. So, it can be observed that v=u1+0u2.

Q: The standard basis S = {ej , e2} and two custom bases B = {b1, b2} and C = {c1, c2} for R? are shown…

A: Given figure is

Q: Define T:R?→R? by T(x) = Ax. Find a basis B for R with the property that [T]B is diagonal. 2 - 4 A =…

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Q: Let V=R2 and let (R?)* be the dual space for R?. Subtask (a). Find the basis {þ1, ¢2} that is dual…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Determine whether the given set S of vectors is a basis for Pn(R). n=1 : S = {2-5x, 3x, 7+x}

A: To determine whether the given set S of vectors is a basis for Pn(ℝ). n=1,S={2-5x,3x,7+x}

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: b) Find a basis for W. c) What is the dim(W)?

A: You want solution for part B and c, So I have given only part B and c. Basis (definition) Subset B…

Q: 53. Consider the basis B of R² consisting of the vectors [3] [F]g = | 1 and We are told that i 93…

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Q: The set B = {3x² – 4, 152² – (20 + 2x), 38 + 4x – 27x²} is a basis for P. Find the coordinates of…

A: Given, the set B=3x2-4,15x2-20+2x,38+4x-27x2 is a basis for P2. We have to find the coordinates…

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: Given the ordered basis B = {p1 =1– 1, P2 = 4 – 7x find [p]B, the coordinates of p = -7+ 10x with…

A: Follow next step

Q: {E] E]} 36. Let W = Span Find an orthogonal basis for W.

A: The solution is given as

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: (b) Find the basis for the col(A) and null(A) 4 5 2 1 30 1 3 2 2 1 A ||

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Q: Do the following vectors form a basis for R³? 1 -2 a. No, the vectors do not form a basis for R O b.…

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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: Given the ordered basis 5 6 ,A2 8 B A1 7 7 4 Аз ,A4 -5 8 5 20 find AB, the coordinates of A = 1 with…

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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: Let S = V = R²; S is a basis for V because Select one: O A. Gy +c,V½ # 0 O B. The vectors are…

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Q: 3. 1 V=R , cat d2= d3=1 1. 2. Tet it be Shaw that basis. Find the Ed1,22,233 in V is a Dual bose at…

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Q: The set S = is an ordered basis for R. Find the coordinate vector of 2 with respect to S 3. 6. 2.…

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Q: The vectors 02 = 6. 03 = form a basis for R' if and only if k +

A: Given vectors are: v1→=4-10,v2→=-666,v3→=24k We have to find the value of k when the vectors form…

Q: 30 175 The vectors B = form a basis. Find the B-coordinates of x = [z]p =

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Q: Define T:R2→R² by T(x) = Ax. Find a basis B for R² with the property that [T]B is diagonal. 3 A = 1…

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Q: thogonal basis for W:

A: Orthogonal decomposition of vector

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.