(b) Find a basis and dimension of the vector space B-C J = where B U = {A € M22 | AB = BT A},

Q: Write the vector v = B - - -3 8 5 -44] 50 24 1 - as a coordinate vector with respect to the basis

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Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: Given: u is a unit vector and the scalar a is positive satisfying the equation au+1,-2,5=0 To find…

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: (a) A: va+v. (b) A: (av). (c) A: √ av.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: W₁ = B W2 = (9) where a ER, BER. (a) Give an expression for ww2 (b) Does the linear independence of…

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Q12: Let vector v = (1, 3) and vector w=(-4,-2). Write vector v as the sum of two orthogonal…

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Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: Let B, D be the following two bases of R³: B = D= 0 0 -2 2 a) Find the change of coordinates matrix…

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Q: Find a representation of the vector AB= (11, -15) in R2 by giving appropriate values for the points…

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Q: Show that in the vector space R³ the vectors x = (1, 2, -1), y = (3, 1, 1), and z = (5, -5,7) are…

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Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: Determine a basis for the vector space spanned by the vectors 3. V1 2 ,V2 .Vs 17 12 O A. {V1, V3,…

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Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

Q: Find a vector with norm 3 that is orthogonal to both the vectors x = Vector: < 1 2 and y = -4

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Q: Decide whether the following sets of vectors span the given vector space, are linearly independent…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: 2 Consider A = -2 null(A). 4 2 2 4 -4 -2 -2 -4 -2 0 1 Give a set of vectors that spans each of im(A)…

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Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

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Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Let V1 MECANIS 3 1 11 V2 = 1 0 V3 = SCAMENTO 0

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Q: Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the…

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