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: Let V= Ips Let B= Ź(1?,3)(0,2),(-2,0,D}be a basis for V. Find the courdinate vector Of the rector X…

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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: Verify that each basis vector of Null(A) is orthogonal to every basis vector for row (A) Find a…

A: Given the matrix ,where B=rref(A).We already have seen that the basis for nullspace of A is And, the…

Q: 5) B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates…

A: A change of basis consists of converting every assertion expressed in terms of coordinates relative…

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: 13. Let A = {a1,a2, a3} be an ordered basis for the real vector space V. (a) Find the coordinate…

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Q: [2 1 1. Let A = 1 1 1 0 2 -1 | 1 Determine a basis for col(A), null(A), row(A), and null(A").

A: Given:A=210-1111102-10 We need to find : (a) Column space of matrix A (b) Null space of matrix A (c)…

Q: 3 1 . A = 1 1 1 1 -2 -2 -2 0 -4 -2 (a) Determine rank A and dim Nul A and justify your answer. (b)…

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Q: 1 Which of the following is a basis of R4that includes the vectors and 1 ? 1 -1 1 1 1 1 1 1 -1 1 1 1…

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Q: 3 -51 -1 . Let W = Span Find an orthogonal basis for 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: Define T:R-→R² by T(x) = Ax. Find a basis B for R² with the property that [T]B is diagonal. - 3 - 3…

A: Given:T:ℝ2→ℝ2 is defined by Tx=AxWhere A=-3-3-1-5To find basis B for ℝ2 such that TB is diagonal.…

Q: 1 1 0 3 9. 1 1 1-2 3 3 2 -1

A: Solution:-

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: 4s -3ss, t in R -t d 12

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Q: Explain why S is not a basis for P2. S = {1, 7x, -6 + x², 2x} O sis linearly dependent. O s does not…

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Q: please explain part d because i am confused by the second and third part of part d.

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

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Q: 8- 3 3 (a) Find the coordinate vector of a = of R³. (b) Let F₁ be the ordered basis of R2 given by…

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Q: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to…

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Q: 0 -88-8 and 0 Find an orthogonal basis for the space spanned by 4 2 6 4

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Q: 1 -1 1 Which of the following is a basis of IR*that includes the vectors and 1 1 1 1

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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: 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: -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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