Example.2 Find a vector that is perpendicular to both A =i+j+k and B = i+j

Q: Let i = [5 3 -2] and i = [0 -4 5]. Find the vector w = 5u – b0 and its additive inverse. [ 13 13

A: Given u→ = [5 3 -2]andv→ = [0 -4 5]

Q: 176 9 Chapter 3. Vector Space- Suppose V1, V2, V3, v4 are vectors in R³. (a) These four vectors are…

A: Given data:- v1, v2, v3 & v4 are vectors in R3.

Q: Example 2: Find the vector equation of the line passing through the point P(2, –4, 3) and…

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Q: v x w = 0 if either v or w ( or both) is the zero vector or v and w areparallel vectors.

A: 1   V x w=0  V x w=0 if either V or w or bothis the zero vector .  Because if one or Both vector…

Q: 1 2 Let vị = V2 = 0 |, and w = 1 be vectors in R- 3 1 (a) Is w in {v1, V2}? (b) Is w in Span{v1,v2}?…

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Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: 2 Let a = -1 | and b = 1 | be two vectors 1 What is |al2|b|2 |a · b[? ?

A: Let us consider the vector v=x1,x2,....,xn then the magnitude of the vector is obtained as…

Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

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Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: Find the state vector that represents the manager's estimate X0 = [        ,      ]

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Q: 16. Let F = 2a, - 6a, = 10a- and G = a, + G,a, + 5a;. If F and G have the same unit vector, G, is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: 15. Determine whether following vectors are linearly dependent or independent 2 3 e2 e3 €4 1

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Q: Example 7: Determine whether the set of vectors in R below is linearly depen- dent? S = {(1,2, 3),…

A: Given set of vectors S={(1,2,3),(0,1.2),(-2,0,1),(1,1,1)} we need to check if the set of vectors are…

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: -41 Question 2: For what value of "a" the vector v = 3 is linear a -3" 国 5 combination of the…

A: Let us cosnider a vector v then it can be written in the linear combination of vectors v1,v2,………vn…

Q: -36 4 3 Express the vector v = as a linear combination of x ar -34 x+ y. %3D ||

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Q: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: Which of the following sets of vectors are linearly independent? 2 - 4 A S = 8. | 1 -3 B S = -1 -3…

A: To determine linearly dependent or independent, we would find the determinant for all the options…

Q: e) The vectors (a, 0,0), (1, a, 0) and (2,3, a) in R³ are linearly independent for all a E R.

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Q: 3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i+j - k Answer +

A: The line through the point (2,2.4,3.5) and parallel to the vector 3i+j-k is .

Q: The figure shows a rectangular box in three- dimensional space that contains several vectors. (The…

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

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Q: 3 -9- 2 : Suppose that vị = 7 V2 = V3 = -3 ,where h is some real number. Consider the following: -3…

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Q: [ - 6 15 Let A Find a vector in R? that is not in the span of the columns of A. 10 25

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Q: 7 6 5 4 Find the vector shown above

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Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: 1: Which of the following vectors are linearly dependent? 21 1 [11 2 A: and 3 C: B: 2 and 4 [3] d 7…

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Q: 10. The set of vectors: [0 1-3 -1], (1 01 1] is linearly independent. Answer: yes or no

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Q: 1: Which of the following vectors are linearly dependent? A: H and 3 B: 2 and 4 C: Ο Α О в O C O D 0…

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Q: 5. Suppose vectors ū and i are linearly independent. Show that the vectors w = 2u+3ū and 7= ū+ū are…

A: if u and v are linearly independent then for au+bv=0 implies a=0 and b=0

Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

A: Given- A=(1,2,0) , B=(3,4,-1), C=(4,5,2) To find the exact value of distance between point C and the…

Q: 2) which of these statements is(are) true?: P: The cross Product is commutative Q: The cross Product…

A: Please follow the explanation in the next step.

Q: a State the condition(s) that a, b, c, and d must satisfy for the vector b to be 1 1 -1 and spanned…

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Q: 1oose the linearly dependent vectors in R. elect one: a. b. -1] C. 1 -2 | d.

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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: How many elements will the vector generated by the command below have? a:(b-a):k*(b-a) 1) 3 2) k…

A: Okk,  In given command,  a - the first element of vector  (b-a) - fixed difference between two…

Q: The following vectors 3 X= 2 2 12 +b 2 are linearly independent if and only if b

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Q: 1. Find the components of the vector. (a) (b) (1, 5) (0, 0, 4). (4, 1) (2, 3, 0)

A: The components of a vector

Q: Example 8: Determine whether the set of vectors in P3 below is linearly depen- dent? S = {1, 4t –…

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Q: (b) If u and v are vectors in R' such that ||ū|| = 1 and |||| = 2 then u · i# 10.

A: The angle between two vectors and Dot product in R3 is related by

Q: х 3 Let A = -5 y 11 If the kernel of A contains the vector what are x, y, and z? -8 2 3 (х, у, 2)…

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Q: x = (1,0, -2, –3) of the vector ||x|| what is the norm? O C) 5 O A) 2 O D) 6 O B) 3 O E) V14

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Q: Example 1: Find the length of the following vectors. (a) = (4, 3) (b) u = (1, 1, 3, 0)

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Q: Which sets of vectors are linearly independent and which are not? 4 2 6. 9 0. 3. 2. 3. 2. 2. 1.

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Q: 9-10. Suppose there are three vectors in R? named vector a, b, and c. If a = b, and b = c, then a =…

A: We need to answer some true and false for  vector space R3  This is answered in the following step:

Q: 3 be -2 Work Problem 2 : Let vi = and v2 = -2 two vectors in R?. (a) ! ! Determine whether v =…

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Q: 10. Suppose A, B, and C are vector functions whereas 1, w, and are scalar functions, which of these…

A: Determine each of the given options for their correctness. Option (A): On the left hand side: ∇∇…

Q: [42 51 W 2 Wa 3 Ws 5 It is g vectors v 30

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Q: (c) Find a vector x so that a 6 c C a b = c |b C + ax C a а

A: