10 -5 14 Let A = 0 2 -6 |and b = 10 . Denote the columns of A by a, a2, a3, and let W = Span (a,, a2, az}. -4 4 - 30 a. Is b in fa,, a2, az}? How many vectors are in fa,, a2, az}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.]

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?

A:

Q: 3 -3 2 6 -3 7 (1.8) Consider the set spanned by the columns of B = 6 3 16 9 -3 21| Please write an…

A: Here,B=3-326-3763169-321∴By reducing B into echelon form by applying row operation, we…

Q: Find the vector PP, 1. Р.(3,2) P, (5,7) 2. P(-2,-1) 3. Р (3,3) P,(4,-5) P, (5,5) 2

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

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: Let A = (4, –4,4, 0) and B = (-4,3, –4, 1) be points in R*

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: What vector v is given by the coordinate vector B = -21 - -5 1 1 -2 -5] -5 4 {JEJEJEJ} -5 3 -1 3 ? 5…

A:

Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

A:

Q: find the diJ tance betueen the vectors

A:

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

A:

Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

Q: Let Is w a linear combination of the vectors V₁, V₂ and 3? choose 13 -14 -4 --[H], -- [5] -- [13] D…

A: Given that the vectors w=-146 , v1=5-4 ,  v2=-4-3 ,  v3=11 .

Q: 19. Given the following vectors: A = 2i-3j+ 6k, B = 8i +2j - 3k and C = i-4j + k. Find * (A+B).C a.…

A:

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: Let a = [3, -7] and b = [-5, 11].

A: given that the two vectors a=[3,-7] b=[-5,11] To plot and check which one is greater.

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: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

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

A:

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

A:

Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

A:

Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

A:

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…

Q: Find the vector determined by 18 || = B = {[.]. 9 6 12 3 9 2 -8 " where B = 3 [-]

A:

Q: Find the magnitude of the vectors represented 3 by (@5 0² 05 + !|

A:

Q: If vector u=2:1+2:/ and vector V =5./+4/, simplify each of the following, writing your final answer…

A: Given:    u = 2i + 2j    v = 5i + 4j

Q: Let A = 10-2 04-6 and b= 0 22 Denote the columns of A by a₁. a2 a3. and let W = Span (a₁. ₂. 3) -48…

A: Part (c) asked and answered.

Q: 7. Given a= [-1, 2,6], b= [0,-1, 3] and c= [2, 4, 5]. Determine a xb.c

A: we are given 3 vectors a, b and c and we need to determine axb.c the vectors are given as--…

Q: Let a₁ = 1 5 -1 a₂ -6 - 25 3 and b = 3 -5 . For what value(s) of h is b in the plane spanned by a,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…