5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find numbers a, 3 and y such that d = 2i + 3j – k can be expressed in the form d= aa + Bb + 7e. %3D

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Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

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Q: 5. Show that the vectors a = 3i- j+4k, b = i- 3j – 2k and c = 4i – 3j+2k are linearly independent.…

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Q: 1.2.4 Prove that vectors (1, 1, 1)", (2, 1,0)", (3, 1, 4)", and (1, 2, –2)" are linearly dependent.…

A: Let v1, v2, v3 and v4 are given vectors that is v1=111  ,  v2=210 , v3=314 and v4=12-2 Claim:    v1…

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Q: Which of the following sets of vectors are linearly independent? OA. B. -1 4 C. -4 -2 ELELEL 9 -6 2…

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Q: 35. The position vectors of the points A and B are OA =2i + j- 4k,OB =-2i +4 j – 2k , a vector…

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Q: c for which the following vectors vi = %3D 1 P4 = are linearly independent. 1

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Q: For what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?

A: t+3  &  2t+c2+2 Now since these vectors must be linearly independent, therefore…

Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

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Q: Consider two vectors →A=Ax^i+Ay^j+Az^k and →B=Bx^i+By^j+Bz^k. Scalar product of these two vectors…

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Q: In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to…

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Q: Which of the following sets of vectors in P2 are linearly dependent? (a) 2-x+4x?, 3+6x +2x², 2 + 10x…

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Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: B. Calculate the first two vectors generated by the Gauss-Seidel method. 1 1 -2] 1 10 4 x={ 15 x(0)…

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Q: linear algebra question:

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Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

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Q: . Show that the vectors a = 3i-j+4k, b = i-3j-2k and e = 4i-3j+2k are linearly independent. Find…

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

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Q: 3 The vectors u = -4 and v = -12 are linearly independent. 6.

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

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Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

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Q: 7. Show that 3-{(; ) ( ) ( )} -1 2 S = 2 1 6 9 is linearly dependent in M22. Write one of the…

A: According to our guidelines I solve only 1 question, so kindly request you to repost the remaining…

Q: For the vectors ü = 2î + 3j – 2k ö = -Sî - 2j – 7k w = 3î + j – 9k the value of [(- ü) x (u – w)].…

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Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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Q: S. The image of the vector i + j – 2k under a mapping (1 2 3 defined by the matrix M, where M = 0 1…

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Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearlyindependent. Find…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.