1. Find the largest possible number of independent vectors among 2 1 1 aj az az a4 a5 = 3 -2 3 345 6 || ||

Q: If u and are the vectors below, find the vector w whose tail is at the point halfway from the tip of…

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Q: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: Are the vectors (1, 2, 3, 4), (2, 3, 4, 5) and (3, 4, 5, 6) lin indep?

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Q: Three unique non-zero vectors a, b, and C are defined by four points in space. Select all of the…

A: Proceed as shown below

Q: Which ONE vector is parallel to (4, 9, 16)? (a) (20, 0, 8) (b) (6, 27/2, 24) (c) (1/4, 1/9, 1/16)…

A: We will find which option is correct.

Q: 5. Express u = (-4, 3, —2) using the unit vectors.

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Q: This question relates to three vectors defined as p = j- 3k, q = -2i -j- 3k and r = 4i + j+ 3k,…

A: To find  The vector product of the given vectors.

Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: 4

A: We are given the following vectors.

Q: Find a general set of solution vectors of х=-5 ха x₁ = x₁ + 3 x ₂ 2 2

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Q: 1. Determine the dot product of the two vectors in the diagram.

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Q: 3) What is the rank of the set of vectors A1 , A2 and Az given by 25 5 A2 = l12] 64 8 %3D [144]

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

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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: 5. Suppose that a, b and care vectors such that |a| = 2, |6| = 1, || = 5, a·b = 0, a. c = 3 and b c…

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Q: This question relates to three vectors defined as p = j- 3k, q =-2i-j-3k and r = 4i + j+ 3k, where…

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Q: Given that 7 write 3 5 7 3 5 -2 2 3 7 -1 2 2 3 3 125 100 010 -5 001 3 as a linear combination of the…

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Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: 4.) Are vectors Linearly independent? 2 3

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Q: 2. Let a, b, c, and d be algebraic vectors in R3, For parts (a) and (b) below, state which theorems…

A: The dot product of the two vectors A→ and B→ is given by the following: A→·B→=||A→||·||B→||·cos θ…

Q: Let a and b be two unit vectors. 1) a x (a.b) 2) a . (axb) 3) a . (a+(axb)) 4) (axb) + (bxa)…

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Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: 1) Determine if the vector b can be written as a linear combination of the vectors a₁, az, and al 1…

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Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: 6. What are the advantages and disadvantages of algebraic vectors compared to geometric vectors?

A: Explanation:

Q: Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

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Q: h 2 S4 2- h 45 LT 2 0 O

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Q: 10. If 3(a, 3, 2)-2(3, b, b) = (-3, 1, -2), determine a and b. Describe the set spanned by the…

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Q: Let A and B be vectors in R" and let c be a real number. Then (1) ||A|| 2 0, and || A|| = 0 if and…

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Q: 1 3 a) Consider a set of vectors, x = |3 |,y = | 2 and z = L4 Can we express the vector, v = 4 as a…

A: The solution is given as

Q: Suppose that u₁ and u2 are vectors with ||u₁|| = 2 and ||u2|| = 3. You are also given that u₁ · U₂ =…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…