For what value or values of the constant u are the following vectors are linearly related and are linearly independent (1-, 1, u, 1), (, 1, u, -1) and (u, 1-, 1)?

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

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

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

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Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

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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: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Two vectors in R- are linearly dependent if and only if they lie on a line through (0,0). Select…

A: It is false.

Q: For what values of the parameter c is the set of vectors (1,1,c), (2,c,4), (3c+1, 3, -4) in R3…

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Q: [C] Is the system of vectors X1 = (2, 2, 1)", dependent? Ху — (1,3, 1)7, X3 = (1, 2, 2)" linearly

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

A: We say a set of vectors v1, v2, ...., vn is linearly independent if…

Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

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

A: Linearly independent

Q: 3. Show that the vectors v, = (0, 3, 1, -1); v, = (6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

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

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Q: Without doing any calculations, explain why the following sets of vectors are linearly dependent:…

A: Since you have posted multiple question with multi part we are supposed to give solution of first…

Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

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

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

A: The detailed solution is given below  Thank you

Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

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Q: If it is known that the internal product of the vectors ā (4, x, -2) and ƃ (1, x + 1,5) is 6,…

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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

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Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: 2. Show whether the set of vectors in R*is linearly independent. Justify your answer. (1, 1, 1,0),…

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Q2: Determined the component of the vectors at each point…

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Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: If there is v1 = (1,3,3), v2 = (0,1,4), v3 = (5,6,3) and v4 = (7,2, -1) is the set of linear…

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Q: Determine if each of the following set of vectors are linearly dependent or linearly independent.…

A: Given query is to find vectors are linearly dependent or indipendent.

Q: Which of the following sets of vectors are linearly independent?

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Q: What is the value of each of the constants that are part of the linear combination between the…

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

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Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Let v1= 2, 5 , 3 ), v, = ( 1 , 1, 1 ) and va = (4, -2 , 0 ) are vectors in R3 then are .a Linear…

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Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

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Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and…

A: The vectors are linearly independent if the matrix formed from these vectors has non zero…

Q: Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k),…

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Q: Determine every c Є R, for which the vectors [c,1,c], [5,c,4], [9,1,c] are linearly dependent.

A: We will use the property of vectors to determine the values of c for which the given vectors are…

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

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Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.