a - b W = a E R3 : a and b any scalar (a) A possible orthonormal basis for W is VA E where A= B= C= D= and E= are all integers such that the entries of the each vector do not have common divisors. (b) A possible basis fort W- is where F= G= are all integers.

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A: The basis for W is:Basis of W= 24-3-8 ,  -1-225

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Q: Q3) Consider the following matrix A, 2 0 -2 -1 0 1 -3 3 |-2 1 A =| 1 1 |-2 0 2 0 -3 2 -1 3 i) Find a…

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Q: (a) determine whether the set of vectors in Rn is orthogonal, (b) if the set is orthogonal, then…

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Q: | Lat T: R R, and S: R + R", *+: a) Find (So 7] and (T o S). (b) Find a basis for the keruel of So7…

A: We have to answer the following for the given maps.

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Q: За + 6b — с ба — 26 — 2с - Find a basis for H = : а, b, с €R -9a + 56 + 3c | -3a + b+ c

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Q: Exhibit a basis for T2, the vector space of all 2 x 2 matrices of real numbers with zero trace.

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

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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.

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Q: Explain why S is not a basis for M2,2- $-{::::)) OS is linearly dependent. S does not span M2,2- OS…

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Q: -2 11 5 100-10 The reduced row echelon form of the matrix A = Find a basis for the null space of A…

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Q: Consider the ordered basis 3 = {1, 1+ x, 1+ x + x²}. Given that %3D [1+ 2л + За?]8 — (а, b, с)*,…

A: Given β=1,1+x,1+x+x2 And 1+2x+3x2β=a,b,ct We have to find value for a,b and c…

Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

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Q: Consider the vector space PA(R) = {ax + bæ³ + ca? + dx + e : a, b, c, d, e E R} of polynomials of…

A: Note:- for this problem you don't mention about f1, f2, f3 (should i have to take  f1, f2, f3…

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Q: - 3x3 + 7x4 = 0 X1 -7x2 - 4x4 = 0

A: The solution are next step is..

Q: The vectors : 1 3 5 2 = = 11 --8-8-6 = 0 7 form a basis for R³ if and only if k k

A: Given vectors form basis for R^3 iff when k=21.Explanation:Three vectors from R3 from basis for  R3…

Q: 4 {BEB]} 0 -2 (a) Basis: Dimension: (b) 12 -277 GOOD 4 -9 -5 11 Basis: 8 - -397 -13 16

A: (a) Given: -211, 000, 4-2-2, 8-4-4. (b) Given: -3-11, 124-5, -27-911, -39-1316. To Find: Basis and…