2.42 Given vector A and second-order tensors S and T with the following components: 8-1 5 4 -7 8 determine {A} 2 {}} 4 = [S] = -105 374 986 (a) tr(S). (b) S: S. (d) A-S. (e) S.A. [T] = (c) S: ST. (f) S.T.A. 6 9 -2

Q: Determine the dot products of the following pairs of vectors. (a) (3, 5), (3, -4) (b) (2, -5, 3),…

A: Solution :-

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: Question 6 Let A' = [-4 16 8] and B' = [-1 x² 21 For which real value(s) of x are vectors A and B…

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Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Determine a so that the vector u= "- [3] is a linear combination u = av+bw of vectors *-[2]· *-6). =…

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Q: 3. Which vector is not equal to zero? a) ix (j×k) b) (ix j) × k c) (i × i) × j d) ix (ix j)

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Find the magnitude of vector v. -1 1 -1 -2 -3 -4 -5 1 2 V ليا 3 + 4 5 (4,-3) K H

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Q: Find the magnitude of the vectors represented 5 3 1 by (a) (b) |³| (c) 12 4 3 LO 5 1

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Q: Which of the following vectors is opposite of the given vector below?

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Q: (1 point) Express the vector = 8 as a sum of the basis vectors x = and y = %3D -13 xt j. = Netes V

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Q: V₁ = V1 V3 = V2= 4 [ 3 [-1] 2 3]

A: We use the properties of linear combination to

Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

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Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

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Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: 6. For the vectors i and i given in problem 1, verify using the dot product that your answer for…

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Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

Q: Find a unit vector in the direction of u and in the direction opposite that of u. u = (-24, –7) (a)…

A: Unit vectors

Q: Let j TE 2 --- = 1 and u = = Write y as the sum of two orthogonal vectors, #₁ in Span{u} and 2…

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Q: Vectors a=(;) b=(;) c=(?) 2a + 3b + 4c = (

A: So here we have to add the matrix by multiplying given conditions so I'm providing hand written…

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

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Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: Express the vector x as a linear combination of the u's. --0-0-0- 0, U₂5, U3 = -50 Select one: O A.…

A: Two matrices can only be added, if the dimensions of both matrices are the same. When two matrices…

Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

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Q: You deposit $2000 in an account with an annual interest rate of r (in decimal form) compounded…

A: Please refer to the solution in next step.

Q: (a) Suppose that a 120-vector a represents the age distribution of the customs in a bank, where a,…

A: (a.) Given: a is a 120-vector that represents the age distribution of the customs in a bank, where…