3. Consider R³ with the standard inner product (i.e. the dot product). Let {(} 1 1 U = span -1 1 2 Find a basis for U-.

Q: 2- Let T:R> R? be the linear opentor def ined X- X27 X2 and let B={uisUz} be the basis for which and…

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. -1 4 4 1 S = = span 1 6.

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. 3 S = span 4

A: In this question, we find the orthogonal set of basis by the Gram-Schmidt process.

Q: Let {u1, u2, u3} be an orthonormal basis for an inner product space V. If v = au1 + bu2 + cu3 is so…

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Q: Let T : Ra[z] → Ra[r] have the following images on he standard basis vectors: T(1) = 1+ 4z –…

A: We have to Find Matrix of T with respect to the standard basis.

Q: In Rª, let S = {(1,2,2, –1), (0, –1,4, 2)} and T = U = sp(S) and W = sp(T). Find a basis for U +W…

A: Your approach is absolutely right!

Q: Consider the following vectors. 6, us Apply Gram-Schmidt to find an orthogonal basis for S. (a) S =…

A: a) S=spanu1,u2 orthogonal basis for s=w1,w2w1=u1=4-10w2=u2-u2,w1w1,w1w1     =381-12-8+016+1+04-10…

Q: Let L be the line given by the span of A basis for Lis 6 in R³. Find a basis for the orthogonal…

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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: 3) If V = R? and neither a, c nor b, c is a basis of R2, show that c 0. %3D

A: 3. It is given that a, c  is not basis of V ⇒c=λa    it is also given b,c is not basis of V⇒c=μb…

Q: et a1, a2 and a3 be colums of A, i.e A = [a1,a2,a3] and let W = span {a1,a2}   Find an orthonormal…

A: Given A=134203166 To find an orthonormal basis of W and distance between a3 and W.

Q: Let QE M,(R) be given such that the columns of Q form an orthonormal basis for R". Prove that Q'Q =…

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Q: 4. (a) Let L be the line in R' spanned by the vector (1,1, 1, 1). Find a basis for the orthogonal…

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Q: Given the basis {(1, 2,−2)T , (4, 3, 2)T , (1, 2, 1)T } for R3, use the Gram–Schmidt process to…

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Q: Let {uj = U2 = 2 be a basis for R². Use the Gram-Schmidt process to find an orthogonal basis under…

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Q: (11) Find the dual basis {V4.V } of the stan dard basis of IR. Let T:IR → IR defined by T(xiy, z)…

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Q: 2

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Q: 3(b) Let x1, X2, ..., Xn be a basis for a vector space V. By generalizing the r produce an infinite…

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Q: 4. Let B = and observe that B is a basis for R³. Using the vectors in 3, find an orthogonal basis…

A: The solution are next step..

Q: .3 Let W = span{x, x' x³, x>} in C[0,1]. Use Gram Schmidt to find an orthogonal basis for W.

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Q: snip

A: (a).               Orthonormalize the set of the vectors                      v1 = 1111 , v2 =…

Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², –1 – 6x + 7x²} O s is linearly dependent. O…

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Q: Explain why S is not a basis for M, 2: -{::}[::} 0 1 1 S = 0 1 1 0 S is linearly dependent. s does…

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Q: (ii) Find the dual basis { V4. } f the stan dard basis of IR. Led T. in 3

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Q: Explain why S is not a basis for R2.S = {(1, 2), (1, 0), (0, 1)}

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Q: Let A = -1 -9 3

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Q: Find the orthogonal complement W⊥ of W and give a basis for W ⊥

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Q: and ŷ = Find the values of y, and y, such that vectors = constitute an orthonorma L0.8337! basis in…

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Q: Consider P2, endowed with the following inner product: 1 1 (p, q) : G P(0)q(0) + G P(1)q(1) + for…

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Q: Recall the vector space P := {a+ bx + ca² : a, b, c E R}, with the inner product defined by (S,9) :=…

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Q: 9. Find a basis for the hyperplane a where a-(2, 1, -3).

A: Any two linearly independent vectors which are orthogonal to the given a are forms a orthogonal…

Q: onsi with its standard product. nat A E Mnxn(R) is orthogonal if and only if, for any orthonormal…

A: since {v1,...,vn} is orthonormal , thenvit * vj=0 if i different than j and 1 if i=j where I wrote…

Q: Let B = {1+t,1 – t} and C = {4, 1 + 5t, t²}. Does B form a basis for P2?

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Q: 8. Let W = Span{v1, v2}. Find an orthonormal basis for W. Vị = -2 , V1 = 4 2

A: An orthonormal basis for an inner product space V with finite dimension is a basis for V whose…

Q: 4.13 Let {u1,u2,..., un} be any orthonormal basis of (where F R or F = C). Show that %3D Euju; = 1.…

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Q: 2: Consider B= a) Show that B is a basis for R³.

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Q: Suppose V = P2 with the inner product p(x)q(x)a Apply the Gram-Schmidt orthogonalization process to…

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Q: Let B = {v1, v2, v3} be a basis for R3. For any u, v E R³ define (u, v) = [u]%[v]B• (a) Is (,) an…

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

Q: - --- Let B = Is Ba basis ofR ? Justify and x = %3D 2 3 3 your answer. If yes, compute xR [x]

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent. O…

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. S = span 1.

A: I am going to find the orthogonal basis for S by using the Gram-Schmidt process.

Q: Use the Gram-Schmidt process to transform the given basis {w1, W2, W3} into an orthogonal basis…

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Q: 2.

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Q: Which of the following is a basis for the vector space R3?

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Q: 1. Use Gram-Schmidt to find an orthogonal basis for R' if B={(2, -5), (1, 3)}

A: Let  V be a vector space with an inner product . Suppose u1 , u2,..., un is a basis for V. Let…

Q: 9. Let i, j denote the standard basis in R2. Find a scalar c if the vector 7i- 2j is perpendicular…

A: Dot product of the two vectors.

Q: Let W = Span(S), where %3D 1 S = 3 -1 Find a basis for W and calculate dim(W).

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.