1. Determine if the following vectors are linearly dependent or independent. Find an exact (non- trivial) linear combination of the vectors that gives the 0-vector (0,0,0) if they are dependent. V₁ = (1, 0, -1) V₂ = (-1, 1, 2) V3 = (-3, 1, 4)

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

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Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

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Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Let (3,-1,2) and (1,4,-1) be co-planar vectors(two vectors that sit in the same plane). Find a…

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Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: check if the given vectors are linearly independent or not . {(-1, 1, 0), (-1, 0, 1), (1, 1, 1)}.…

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Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3, 2, 1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

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

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Q: Which of the following sets of vectors are linearly independent? A. (4, 8,-5), (-9, -4, -6), (-13,…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

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Q: Find two linearly independent vectors perpendicular to the vector 2 -5 -9 D =

A: Two vectors are said to be perpendicular to each other if and only if their dot product is zero.

Q: 3.- Define the vector that allows the linear combination and if it exists, demonstrate the linear…

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Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , č = {0, – 1, 2} and (ii) ā =…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…

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Q: Q4. Determine whether the vectors are linearly dependent or independent. v1=(4,-2, 2), v2 = (5, 4,…

A: v1=4-22, v2=54-3, v3=-793 We have to check whether the given vectors are linearly dependent or…

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…