The following question is from linear algebra : Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step.

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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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: Let u = 4i + 5j, v = -4i +2j, and w = 3i - j. Determine the i, j form of each of the following: (a)…

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

Q: Compute (u v Ղա • Ա. . — u = (i, 7,6), v = (2, -7i, 1+i), w = (7-i, 7i, 3 + 6i) u · v) ա • Ա —

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Q: 3. Solve the system below using the specified method. Write your answer in vector form. X1 - 3x2 = 2…

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Q: Find a vector orthogonal to both 7 -10 and w -10 -10 -4 7

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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: Find the coordinate vector of x2 + x - 17 relative to the basis {x² + 1, x + 2, x - 3}.

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Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

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Q: Show that vectors (86, 87, –46), (-8, –6, –2), and (-6, –7, 6) are linearly dependent-that is, there…

A: If vectors are linearly dependent then they can be expressed as a linear combination of each other

Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: Find the vector x determined by the coordinate vector ---(DBE) 8 and the basis B = 0 XB = The vector…

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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: 3. Find all real values of c such that the vectors and e+3 are linearly independent.

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Q: f possible express the vector v as a linear combination of 1, V2, and V3. b) v = (0, 0, -1), V₁ =…

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Q: Find the matrices of the following linear transformations from R³ to R³. The orthogonal projection…

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Q: Find a vector orthogonal to both v = 8 -6 and w 9 0 -6

A: Step 1: The cross product of two vectors is orthogonal to both of the original vector Step 2: Step…

Q: (a + n ) ² − ( ₁ + n ) z

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Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: -1 X1 Let v = Find a vector x = x2 such that 3v +x = |2|

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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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