Question 2 2a+ b a a, b, c eR be a subset of M22. Let W=- —а- 2b а+ b+c (a) Find a basis for W. (b) What is the dimension of W?

Q: Let b = (2, -4, 2). Let W be the hyperplane b-. (a) What is the dimension of W? (b) Find a basis for…

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Q: 3 9 A -2 -3 1 9 Find an orthonormal basis of the image of A.

A: Orthonormal basis of a vector space V is a basis of a basis for V whose vectors are orthonormal. Two…

Q: The set F = {1+t,t +t, 1+2t+t2} is a basis for P₂. Find the coordinate vector of p(t)= 3 +t-4t²…

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Q: The vectors -5 FB-B-B , V2 = 6 -2 form a basis for R³ if and only if k| V1 = 3 -6 0 and V3 = 1 -6 k

A: Given that the vectors v1=3-60 ,  v2=-56-2   and v3=1-6kThe matrix form of the given vectors is…

Q: 3 -51 -1 . Let W = Span Find an orthogonal basis for W.

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Q: The vectors 7 -6° Ú2 = 2 -3 form a basis for R³ if and only if k + Submit answer

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Q: 2 4 -2 -1 W = span({ 0 }) -1 -2 (a) Find a basis B for W. (c) Write down the dimension of W.

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Q: -B 2. Given: A = 2 -4 0 2 1 -1 2 1 2 3 1 -2 1 4 4 a. Transform A into RREF then give a basis of its…

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Q: Determine whether {v1, v2, V3} is a basis for a3. R V1 4, v 2 = V 3 = -4 8 -8 -24 Yes No

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Q: 2 Determine whether the vectors form a basis for R*. (You may use any relevant theorem that we have…

A: A basis for a subspace S of Rn is a set of vectors in S that is linearly independent and is maximal…

Q: B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates of…

A: Given that B = 1 , 2 , 0T , 1 , 1 , 1T , 1 , 0, 0T is an ordered basis for ℝ3 .  We have to solve…

Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: -2 4 -21 A = -4 -1 -2 -2 1 A basis for the image of A is { }. To submit your answer, you may enter a…

A: Notice that :   In given matrix, (row 3) + (row 1) = (row 2) and row 1 and row 3 vectors are…

Q: Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the…

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Q: a b -10 Let W = = € M₁x1 a, b, c, d = R, a + 4b - 3c = 0, and b+2c-d = 0) : (a) Show that every…

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Q: How do I find a basis for {(2c, c, b)} | b, c ∈ R}? I tried writing it as a linear combination and I…

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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: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

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

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Q: Question 4 (a) Let T:R'→R' and a {e.e,.e,,e}. be the standard basis of R' and B={v,v,,v,} is some…

A: Note that, here  the elements are row vectors operate from left side,

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 3x + 4x²} O s is linearly dependent. O…

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Q: 11. Jack and Jill took a linear algebra exam. One of the questions was the following: Question: Let…

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Q: Explain why S is not a basis for P2. S = {1 - x, 1 - x², -1 - 4x + 5x2} O sis linearly dependent. O…

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Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1) form…

A: 5) Given  that  Let, So we have  .Hence Noted that .Because  Hence basis for subspace V of  is

Q: -4 2 • Let W = Span 2 find a basis for W+. 8 -4

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Q: Let 1 -6 -2 A 1 -3 1 3 -8 4 Find an orthonormal basis of the column space of A.

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Q: nd a basis for the set of all vectors of the form below, where a, b, c are real numbers. [ a-2b+5c,…

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Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: -3 2 0 , В :).B = -2 2 -2 1 Let A = (, -1 -4 3 -4 5 -6 3 a) Find a basis for null(A). b) Find a…

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