Linearly In-dependency and Dependency 5. Determine whether or not the following vectors i R³ are linearly dependent: • (1, –2, 1), (2, 1, – 1), (7, –4, 1) (1, 2, –3), (1, –3, 2), (2, –1, 5) • (1, –3, 7), (2,0, –6), (3, –1, – 1), (2, 4, –5) • (2, –3, 7), (0,0, 0),, (3, –1, –4)

Q: Which of the following sets of vectors in R are linearly dependent? Note. Mark all your choices. O…

A: Let us consider a set of vectors v1,v2,......,vn then the set is linearly independent if…

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: 4. State with a brief explanation whether the following statements are true or false. (a) The…

A: a) true The vectors (1 ,0) and (0,1) is linearly independent. We know that linearly independent set…

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

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: Determine (if they exist) the values ​​of the parameters α and β so that the vector (4, 9, -57, 17)…

A: this is the question of vector  and here the summation of vector is given  we have to find the value…

Q: Determine whether S = {(1, 1, –3), (–1,2, –3), (4, –1, –2)} is linearly dependent or linearly…

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Q: Determine whether the set of vectors in R3 is linearly independent or linearly dependent. S = {v1,…

A: The given set of vectors S=v1, v2, v3=1, 2, 3, 0, 1, 2, -2, 0, 1. We have check whether the vectors…

Q: (7,1, –4, –2,3). Find the components of the (a) Let u = (1, 2, –3, 5, 0), v = (0,4,–1,1,2), and w =…

A: Let u→=1+2j^-3k^+5l^      v→=4j^-k^+l^+2m^      w→=7i^+j^-4k^-2l^+3m^Given:-…

Q: 3 Determine whether the vector w = | 10 is a linear combination of the vectors v1 = 0 , v2 = -2 -3…

A: Our Aim is to determine whether the vector w=310-1 is a linear combinationof the vectors v1=101,…

Q: For what value or values of k the vectors V1 = (1,0, –2,0), V2 = (-1,k,–2,0), V3 = (1,1,1,2) are ▼4…

A: A set of vectors are linearly dependent if there exist scalars not all zero such that  . A system…

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

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: Determine whether each of the following sets of vectors are linearly dependent or linearly…

A: Kindly refer to Step 2 for the solution.

Q: Find the vectors T, N, and B at the given point. r(e) = (1², 31³, c), (1, -3, -1)

A: Given: and the point.The point occurs at t=-1.We have to find T,N and B at the given point t=-1The…

Q: 3. In R³, consider v₁ = (1,0, -1), V₂ = (1, 0,2), V3 = (0, 1, 1), №₁ = (1, −1, 1). (a) Show that any…

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Q: Let = (1,2) and 7=(3, a) be two vectors in R². (a) For which value of a the two vectors an are…

A: Vector is parallel to another iff one is constant multiple of other .example: u=kv Orthogonal when…

Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: 21 -2 and y -3 3 Express the vector v as a linear combination of a -4 y.

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Q: 5. v₁ = (1, 0, 0), V₂ = (0, -2, 0), V3 = (0, 0, 3)

A: The given vectors are as follows:To Find:whether the given vectors u and v are linearly dependent or…

Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

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