Consider the vectors v, V, V3, and b. 2. 4V2 4 V1 Vg 6 ,b 7 b = | [8 9.

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

A: We have to find which formulas involving vectors  a→,b→,c→ and vector a→ does not equal to zero…

Q: Which of the following vectors is parallel to the line 7x+ 14y = 20? %3D (-6,3) (8,-16) (2,4) 0.…

A: We first find the slope of the line using y=mx+b form

Q: For the given vectors v and w find: (a) v+ 2w (b) 3v - w (c) 2v - w+u

A: We can use the geometry of vectors to find these as shown ahead.

Q: For the given vectors u andi, find the value of u v and normalize 1. u = (2,7,–1,20), 2. ü = (3,…

A: The dot product and addition of two vectors is given by Given…

Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 1 - 6 2 - 1 V2 = - 3 3 1 The…

A: Solution

Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: We will first assume a=(a_1,a_2,a_3),b=(b_1,b_2,b_3) and c=(c_1,c_2,c_3).Now will will use…

Q: Determine the value of k for which the vectors u and v are orhogonal u = (1, k, –3), v = (2k, –5, 6+…

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Q: Q6) For which values of x are the following vectors linearly independent? 2 3 w = 1 %3D -2 1

A: We have to find the value of x where u,v and w are linearly independent

Q: Q1:The following vectors; Ā =, B =< 2,-4,6

A: To find the cross product of the vectors  A⇀×B⇀=ijk14-12-46 simplify…

Q: 2 x=| 2 as the linear combination of the vectors u 1 Write your answer in the form x=av+bv+cw for…

A: Topic:- vector algebra

Q: sketch the vectors −→AB and −→P Q, and determinewhether they are equivalent  A = (5, 8), B = (1, 8),…

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Q: 4. Let Ā = -(1+ m)î + 7j – 5k ,B = xî + (6 + n)j – 2k and C = (8+ m)î – 2k , find the following:…

A: Given data is : A→=-1+mi+7j-5kB→=xi+6+nj-2kC→=8+mi-2k

Q: If v=3w then the two vectors v and w are ................

A: Given :                    If v = 3w, then the two vectors  v and w are ____________

Q: Given the vectors u=, v= find u+3v| 3. 15 -1

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Q: Find the best approximation to z by vectors of the form c,vi + C2V2. 2 - 2 V2 1 4 3 2 The best…

A: We have to find out the best approximation to z by vectors of the form C₁ V₁ +C₂V2.

Q: Which one of the following vectors is perpendicular to the line L: 2x +3y- 6= 0 O 2i- 3j O 21 3j

A: concept:  a line ax+by=c has perpendicular vector &lt;a,b&gt;

Q: 4. Let Ā = -(1+ 2 )î + 7j – 5k , B = xî + (6 +0)j – 2k and Č = (8 + 2 )î – 2k, find the following:…

A: A = -(1+2)i + 7j -5k = -3i + 7j -5k B = xi +(6+0)j-2k = xi + 6j -2k C =(8+2)i  -2k = 10i -2k

Q: W If the vectors in the figure satisfy u= |v=1 and u + v +w = 0, then what is w?

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Q: For what value of x, are the vectors vị 3 V2 = 3 and v3 = 2 linearly dependent? 3 Select one: 10 9.…

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Q: For the vectors u = (3, 2, 1) and v = (1, 2, 0), evaluate the following expressions. a. 2u+ 4v b. 4u…

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Q: Which value of m would make​ p(x)=mx+5 and​ q(x)=2x+1 linear dependent vectors in​ P_1(x)?   A. 5 B.…

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Q: Given the vectors vi = (1,1, –1), v2 = (1,2,3) and v3 = (0,1,1). S = { v1, v2, v3} set R3 does it…

A: 3 vectors span R³ if they are linearly Independent. Vectors are linearly Independent if their…

Q: 3. For the vectors d = (2,11, -3) and 7 = (-7,0, –1), find proj, d.

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Q: 41. For what values of t are the following pairs of vectors parallel? (a) 27 + (r² + 71 + 1)j +ik,…

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Q: d) Determine if the vectors t² + 2, 2t² +t+3, 3t² + 4t +5 span P₂. 1 2 0 1 3 b) Determine if the…

A: A set of vectors S is called a basis of  a set P if  (i) the set S is linearly independent (ii) the…

Q: Consider the vectors V1, V2, V3 and b. 1 2 8 -2 V1 ,V3 -13 6. 12 18 Write b as a linear combination…

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Q: In R, you are given the vectors -10 u = 4 and v = -7 -39 If w = -9 belongs to Span(u, v), then what…

A: Consider the provided question, vectors,u=-34-4  and  v=-10-7-4and if w=-39-9z  belongs to Span…

Q: 19. For two non – zero vectors ā' and b,if ||a' + || = ||a'||, then which of the following is…

A: Given : For two non-zero vectors a→ and b→,  ||a→+b→||=||a→|| Use the property ||a→||2=a→.a→

Q: Find the best approximation to z by vectors of the form c, v, + C2V2 4 -7 1 1 V2 = 2 z= 3 [-1] 4 1…

A: To find  The best approximation to Z by the vectors of the form c1v1+c2v2.

Q: Write the vector 3 (if it is possible) as a linear combination of the vectors d1, d 2.

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Q: 6. Given the following vectors, Draw: a) a-b b) 2c + a c) - (c-b) a X b of

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Q: Q1) A) If U and v arn 2x1 orthnormal vectors and A =UV", the the brace of Aequal 6o A1 8-1 c) 2 d)o…

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Q: Let vi = 2 v2 , V3 = -3 3 Does the set of vectors {v, ,v2, v3} span R3 ? Give reason(s) for your…

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Q: Consider the vectors V1, V2, V3, and b. V1 4 V2 = 5, V3 6 ,b = 7

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Q: Given the vector component of D(2, – 6, - 5) and G(1,2,3), find the vector of D that is parallel to…

A: Given vectors D(2, -6, -5) and G(1, 2, 3) We need to find the vector of D that is parallel to G

Q: What is the value of B for the vector [2, 4, -6]? O a) 74.5° O b) 57.7° O c) 143.3° O d) 36.7°

A: Given vector : [ 2, 4, -6 ]. Compare the vector with [ x, y, z ]. Therefore x = 2, y = 4 and z = -6.

Q: 4) Which of the following vectors is parallel to the line L: x = 1 -t, y = 2 + 3t, z = 5 + 2t? a)…

A: According to the guidelines we are answering first question. Please repost the remaining.…

Q: Which vector is not a linear combination of x, y and z? 1 X = 1 y =| 0 z = 1 -2 3 -1 1 -3 -1 3.

A: To check  the given question the set of vectors is linear combination we proceed as follows

Q: For the given vectors v and w find: (a) v + 2w (b) 3v – w (c) 2v 3 - -w + u 2

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Q: Consider the following vectors: 2 -2 and b -3 u , V 4 When b is expressed as a linear combination…

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Q: Find the best approximation to z by vectors of the form c, v1 + C2V2. 3 3 6 15 - 1 V2= - 1 z= - 3…

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Q: Find the best approximation to z by vectors of the form c, v, + C2v2. 2 4 2 V2 Z= 2 The best…

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Q: Find the vectors T, N, and B at the given point. r(t) =&lt; t2 ,(2/3)t3 ,t&gt;   ,  (4,16/3 ,2)

A: Consider the given vector function.

Q: Find the best approximation to z by vectors of the form c,v1 + C2V2. 2 2 6 - 2 V1 = V2 - 1 1 4 2 The…

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Q: Consider the following vectors: -3 4 4 4 1 , v = 1 , w = 2 |, and b = -4 u = 3 3 When b is expressed…

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Q: Which vector is not a linear combination of x, y and z? 2 X = 1 y = z = 1 -2

A: Given: x=21-1 ,y=101,z=11-2 Let's check all option  (i) 0-13 Let's choose scalars 0,1,-1, then…

Q: Find the vectors T, N, and B at the given point. r(t) ) =(2², ²32²³, t), (4,- 15, -2) N = B =

A: This question can be solved by applying the formula of T,N,B

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.