Let B= = : {b₁, b₂} and C = {c₁, c₂} be bases for a vector space V, and suppose V = b₁ b2 = [v] = [B\C [v]ε] = 7b₁ + 4b2 -C1 +9c₂ 7c₁

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: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: 4- Determine whether the vectors v1 = (1, –1, 2), v2 = (3, 2, – 1) and v3 = (5,0, 3) form a linearly…

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Q: IP IE Express the vector + =[] y as a linear combination of = [2] -[1] and y=

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Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: Consider the vectors u₁ = [1,0,-1], u2 = [1,0,0] and u3 = [0, 1,1], v= [5, 1,3] and w= [1,0,3]. (a)…

A: As per guidelines of Bartleby i am supposed to solve on first three part,if you want more solution…

Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: The objective of the question is to verify if the vector w is equal to the sum of the vectors V1,…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Determine the real value/s of c such that the following vectors are linearly independent: 4 - 2 -6 6…

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Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

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Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

Q: }] respectively. Let y = and u = . Write y as the sum of two orthogonal vectors, y, in the span of…

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Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

Q: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

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Q: The vectors v1,V2.Vn in a vector space V are said to be linearly dependent if CV+C2V2+.…

A: By using definition of linearly dependent and independent.

Q: Find the value of u that make the set of vectors {a, b, c, d} linearly dependent. [1 2 1 1] b = [0 1…

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Q: Consider the vectors u₁ = and the vector w = 3 H Q- W U2 = []} Uz = U2+ →→→→ →→→→ If u IS in the…

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Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

A: Here, v1,v2,v3 is an orthogonal set of vectors in R5 and w is a vector in Span(v1,v2,v3) such…

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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Q: Let T: R2 R³ and u, v E R2 such that T(u) = 1 2 -2 and T(v) = 4 -2 1 Find the image under T of the…

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Q: Find all values of b such that the set of vectors {(1, 1,0), (b, 1,0), (0, 2, 3)} is NOT independent…

A: The given set of vectors:  110 , b10 , 023

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

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

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Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: Suppose {V1, V2, V3} are linearly independent vectors in a vector space V. Find the number(s) k such…

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