If u =<1,0,0,0,0),v=(0,2,0,0,0),w=(0,0,4,3,1>,x=(0,0,7,5,0) are linearly independent then they will form basis for RS. O True O False

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

A: The answer is given below:

Q: i) Find the matrix of T with respect to ordered basis B' = {(1, 1), (1, – 1);:.

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Q: If u =,w=0,0,4,3,1>,x=(0,0,7,5,0> are linearly independent then they will form basis for R5. True O…

A: the objective is to state true or false.

Q: Find a standard basis vector that can be added to the set {v1, v2} to produce a basis for R° a. V1 =…

A: To find standard basis vector

Q: Show that ?? = {(1,2,3), (−1, −1,1), (5, −4,1)} is an orthogonal basis of ℝ3, and use the Fourier…

A: Definition: A subset of a vector space V is linearly independent, if  Theorem: If is a orthogonal…

Q: A set of vectors in V is linearly independent if and only if they form a basis for V. True False

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Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: Let A € Mnxn (R), & be the standard basis for R", and B = {₁,...,n} be another basis for R". If P is…

A: Given, a matrixA∈Mn×n(ℝ). Given, ε as the standard basis ofℝn and  β={v1,v2,...,vn} as another basis…

Q: The Gram-Schmidt process transforms the basis u=(1, 2), U2 =(6, 2) of R into the orthogonal basis…

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Q: Explain why S i not a basis for P2. S = {1, 4x, -5 + x?, 3x} O sis linearly dependent. O s does not…

A: We have to find out

Q: (16v2,2v2) is any B = {(, -),,)} be an orthonormal basis for R. If Let vector in R, determine the…

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Q: 1 Let u₁= = U₂ = U3 = 1. and y 3 3 1 (a) Show that {u₁, U2, U3} is an orthogonal basis for R³. (b)…

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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: Explain why S is not a basis for P,. S = {1 - x, 1 – x?, -1 – 2x + 3x?} O sis linearly dependent. O…

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Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

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Q: 4. Present the standard basis vectors e, and ez in R? as linear combinations of (3, 1) and (1, 3).

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Q: 5/ Find the coordinates of x = with respect to the basis consisting of uj = (1, 3, 2), u2 = (2,…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Explain why S is not a basis for M2,2- s={: :}[::} 1 0 0 1 O sis linearly dependent. O s does not…

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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: -3' 2, uz [3] -4 is an orthogonal basis of R3 and x = 2 Let u1 1, u3 4 If x can be expressed as a…

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Q: Let S = {vi, v2, v3} where v = (1,0,1), = (1,1,0) and (0,0,1) be a basis of R³. Let T = %3D %3D %3D…

A: Given: PS,T=12-111-1221S=1,0,1,1,1,0,0,0,1

Q: The vectors x1 = (2, -3, 1), x2 = (1, 4, -2), X3 =(-8, 12, –4), x4 = (1, 37, -17), and x3 = (-3, -5,…

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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: If the vectorsV1,..., Vk form an orthonormal basis of OC", then they also form a basis of R*. O True…

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Q: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: Find the coordinates of (2, 3, 4, – 1) with respect to the basis B = {(1, 1, 1, 2), (1, –1, 0, 0),…

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Q: Is R={(2,0,1), (2,-1,1), (4,2,0)} a basis for R²? Yes or No? Justify or give/find a counterexample.…

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Q: 15. Use the Gram-Schmidt process to transform the basis {r1, x2, a3, T4} into an orthogonal basis…

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Q: Let S = {u1, uz2, U3, U4} C Rª, where (1,1, 1, 1), U2 = (1, 1, – 1, –1), (1,—1,1, —1), и4 — (1, –1,…

A: As per the guidelines I solved your first three subparts of the question. For more solutions please…

Q: 0.1,1 ) and v (0, 0,1) is Basis of R3 Not spannig Linear dependent

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Q: Let X1=[1,0,2,-1] , X2=[-1,1,0,1] , and X3=[2,0,0,-2] and let W= Span{X1, X2 , X3}. Find an…

A: Concept: According to the Gram-Schmidt process, uk→=vk→-∑j=1k-1projuj→(vk→)uk​​=vk​​a vector…

Q: 2 then the is the matrix of transition from the base B to the basis B' and the coordinates of vector…

A: Given that B and B' are bases of a vector space v and P is the matrix of transition from base B to…

Q: Prove that a linearly independent system of vectors v1, V2, . .. , Vn in a vector V is a basis if…

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Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

Q: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: 2.) Determine whether S = is a basis for R³. If it is write u = (6,3,6) as a linear combination of…

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Q: Let B = uj = ,U2 = and C = , V2 = Find Pc, the transition matrix %3D from the standard basis of R2…

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Q: Determine whether or not the set of vectors S-(. l where -(1,1.1), - (1,2.3).-(2,-1,1) form a basis…

A: The subset S is basis of vector space Rn over field R if  S spans Rn and  S is linearly independent…

Q: Explain why S is not a basis for P2. S = {1, 6x, –7 + x², 8x} S is linearly dependent. O s does not…

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

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Q: If {v1,..., Vn} is an orthonormal basis for R", then vịvi + · · ·+ vnvn = I. O True O False

A: Given, v1, v2, ..., vn is an orthogonal basis for Rn. then v1v1T+...+vnvnT=I It is True or False. To…

Q: Explain why S is not a basis for P2. S = {1, 6x, –5 + x², 8x} O sis linearly dependent. S does not…

A: Basis: A non-empty subset B of a vector space is basis if a) B is linearly independent b) B spans V.…

Q: Let Find an orthonormal basis of the column space of A. 2 5 3 -5 3 2 us

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Q: i) Find the matrix of T with respect to ordered basis B' = {(1, 1), (1, – 1)} %3|

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Q: Explain why S is not a basis for P2. S = {1, 8x, -6 + x², 3x} O sis linearly dependent. O s does not…

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Q: 3. Do the vectors (1, 1,0), (0, 1, 1) and (1,0, -1) form a basis of R3?

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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: |– 1/V5 29) Let u,= 2/ 5 2/V5 [1/v5] Show that {u1,u,} is an orthonormal basis for R².

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