2) Suppose the vı, V2, V3, V4 is a basis for a vector space V. Prove that vị + v2, Vz + V3, V3 + V4, V4 is also a basis for V.

Q: 2, Xz} is a basis of V, (R). show that {, +X, X2 + X3, X3 +Xi} is also a basis of V, (R),

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Q: 4. Find a basis for R3 that contains the vectors (1, 2, 3) and (3, 2, 1).

A: Note : according to our Company guidelines we can answer only first question, please repost the…

Q: snip

A: The basis in n-dimensional space is called the ordered system of  linearly independent vectors. Let…

Q: If A = {v1, v2, ..., vn} be a basis for FV and n ≥ 2 then, is B = {v1+v2, , v2+v3, ..., vn+v1} also…

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Q: 4. Prove that ū = (1,0, 1), ở = (2, 2, –1) and w = (-2,3,0) are a basis for R. Use these three…

A: Given u=(1, 0,1), v=(2, 2,-1), w=(-2, 3,0)  To check they form a basis for R3 or not.

Q: Let {u1, u2, u3} be an orthonormal basis for an innerproduct space V and letu = u1 + 2u2 + 2u3 and v…

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Q: Write the standard basis for the vector space.M3,3

A: The set of  all nXn matrices with real entries is a vector space and is denoted by Mn,n . Standard…

Q: Extend the vectors [1 3 -1 -1]' and [0 -1 1 1]' to a basis for the following vector space. V = 6- 2a…

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Q: Let {u1, u2, u3} be an orthonormal basis for an innerproduct space V. If x = c1u1 + c2u2 + c3u3 isa…

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Q: Q2. Leb u, and v be two livearly ondependent vecetors in R? Do thiy necussavily form a basis of R?

A: We have to write about vector u and v

Q: 13. Do the set of vectors S = { x²+2x-4, 6x² +7x+3, 2x²+x) a basis for P2? Refer to the definition…

A: The given set is;  S=(x2+2x-4, 6x2+7x+3,2x2+x).

Q: If a vector space has one basis that contains infinitely many elements,prove that every basis…

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Q: Find a basis for the space spanned by these vectors:

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Q: 11. Consider the vector space generated by [1, 1,1, 1), [1, 1, 2, 4), (1,2, -4, –3). Find an…

A: Note: according to our guidelines we can answer only 11 th question

Q: It can be shown that the vectors u1 = (2,−3, 1), u2 = (1, 4,−2), u3 = (-8, 12,−4), u4 = (1, 37,−17),…

A: A basis is a subset of a vector space that spans the vector space and is linearly independent.

Q: Let S ={v1 , v2 ,...,vk } be an orthonormal basis for the Euclidean space V and {a1 ,a2 ,...,ak } be…

A: Given: S=v1,v2,,....vk is an orthogonal basis for the Euclidean space V. Also, a1,a2,...,ak is any…

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Q: 14 - Which one is a basis for the vector space R3 ? 1

A: We have to check

Q: 2 Find an orthogonal basis for the space spanned by 4 and

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Q: Suppose that V is a vector space with a basis {x1, x2, x3}. Show that {x1 + x2 + x3, x2 + x3, X3} is…

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Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

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Q: 19. Prove that the set {(1, 0, 0), (1, 1, 0), (1, 1, 1), (0, 1, 0)} spans the vector R' (R) but is…

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Q: 2. Show that the set S = {P1, P2, P3} is a basis for P2 (space of polynomials of degree less or…

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Q: Let A = {v1, v2,.., Vn} be a basis for FV and n > 2. Is B = {v1 + V2, , V2 + V3, ..., Vn + v1} also…

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Q: Let {a1, a2,..., an} be a basis of a vector space V, n > 2. Show that {a1, a1 + a2,...,ɑj + az + ·……

A: We will be using basic definition

Q: 8. Prove that ū = (2,2, 1), ī = (-1,0,1) and w = (-2,3,0) are a basis for R³. Use these three…

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Q: Show that the vectors (1, 1, 2), (1,2,5), (5,3,4) of R'(R do not form a basis of R'(R).

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Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: Assume that: U1= -1 -1 u2= 1 And W=span {U1, U2}. -Find a basis to W-.

A: Here   u1 , u2 are two vector. W= span {u1, u2 } So, {u1 , u2 } is a basis . Now we found a basis ,…

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

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Q: Let (ẽ1, 2, 23, 24, 25, 26} be the standard basis in R6. Find the length of the vector x = 4ẻ₁ – 4ẻ2…

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Q: Show that {u, U2}, {u1,u2, U3} is an orthogonal basis for R? or R°, respectively. Then express x as…

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Q: 4 コ 2 %3D 1

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Q: Show that B = {v1=(1,0,0), v2=(3,7,-2), v3=(0,4,1)} is a basis for R3

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Q: 3. Find a basis among the vectors [1, 2, 3], [2, 6, 10], [0, –3, –6],[-1,-3,-5] (which are surely…

A: Q3 asked and answered.

Q: Determine whether S is a basis for the indicated vector space. S = {(0, 2, 0, −1), (0, −1, 2, 0),…

A: To check whether S is a basis

Q: Show that the set S = {p1.P2-P3} is a basis for P2 (space of polynomials of degree less or equal to…

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Q: 1) Suppose v1, V2, V3, V4 span a vector space V. Prove that the list vi - v2, V2 – V3, V3 – V4, V4…

A: Spanning set of the vector space

Q: 5. Find a basis of R' containing the vector (1, 1, -2)' and (1, 2, -1)".

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Q: Let (₹1, ₹2, ₹3, ₹4, 25, 26} be the standard basis in Rº. Find the length of the vector x = -22₁ +…

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Q: 4 2 If a basis for R3 is B = and if a vector in the standard basis is i = |-4|, find its 5…

A: We know, The set B of vectors in a vector space V is called a basis if every element of V can be…

Q: 23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.

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Q: Find a standard basis vector that can be added to the set {V1, v½} to produce a basis for R а. 0 —…

A: We have to solve given problem:

Q: Let -3 be an orthogonal basis for a

A: Introduction: It is given that 4-30, 005 is an orthogonal basis for a subspace W. We have to find an…

Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (2, 1, 3), (3, 4,…

A: S= {(0,0,0), (2,1,3), (3,4,2)} We need to find if S is a basis for vector space R3

Q: ´) Consider the vectors - - (-) · · - () ₁ - - () a= 2 Do these vectors form a basis of R³? If yes,…

A: They form a basis for R3. Explanation is as follows

Q: Show that the vectors (1, 1, 2), (1, 2, 5), (5, 3, 4) of R'(R) do not form a basis of R'(R).

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Q: If W is the sub space can find and orthogonal basis for a W

A: Given set is  w=span1-1100,-10001,10011,10001 Let  v1=1-1100, v2=-10001, v3=10011, v4=10001 Let us…