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Q: A(x + y) = Ax + Ay. 2. A(ax) = a(Ax) = (aA)x

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Q: The ODE (x dy/dx = yx²) is separable. true false If for a square matrix A and B, null matrix O, AB =…

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Q: Determine whether the following matrix is orthogonal or not: cosa sina A = sinßsina cosß -sinßcosa…

A: To determine if a matrix is orthogonal or not, multiply the matrix by its transpose. If the…

Q: Let A= 00 b) Say if A is diagonalisable sur Cv H E M3x3(C) such that H-¹AH is diagonal.

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Q: The determinant of a second-order tensor is also defined by the expression [(S · A) × (S · B)] · (S…

A: We will verify the given identity in 3 dimension, and by choosing A,B,C as our orthonormal basis.

Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

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Q: 3. Give an example of an orthonormal set with 4 non-trivial vectors in R5.

A: We have to solve given problem:

Q: Let 02 A = (-23). 4 Find the Jordan normal form J of A and give a matrix P such that J = P¹ AP.

A: We have to find the Jordan normal form J of A and also give a matrix P such that J = P-1AP

Q: 1. True/false: all linear functions U:M_(3x2)(F)->F^6 are isomorphisms. 2. True/False: If P and Q…

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Q: Let 0.5 0.5 -0.5 0.5 -0.5 0.5 üz = -0.5 0.5 0.5 -0,5 -0.5 -0.5 Find a vector ig in R' such that the…

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Q: Please provide detailed solution for II part asap to get a upvote

A: Given - Let A, B ∈ Mn,nℝ be two square matrices. To Prove - Prove that if the matrices A and B are…

Q: Prove that if A is invertible, then 1 det (4) det (4-¹) = -

A: We have given that a square matrix A is invertible. To show that detA-1=1detA. We know that an…

Q: iii) Give an example of two matrices A, BE M22(C) such that A) A is not similar to B; and B) PA(:) =…

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Q: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: Find all values of a for which the given vectors form basis for R' a? u = V = and w = a 1 2

A: given vectors u=a201 , v=0a2  and w=101 claim- find all the values of a for which the given vectors…

Q: If uHu = 1 show that I -2uuH is Hermitian and also unitary. The rank-one matrix uuH is the…

A: As per the question we are given a unitary matrix u (so that uHu = I) Now we have to  Show that I -…

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: tind the equation of a polynomial Shose graph, passes through the points t-1,7), (0,2)(2;4)

A: As per guidelines I had solved the first question. Thank you.

Q: Suppose T: R¹→P3 is a linear transformation whose action on a basis for R4 is as follows: -3 0 ਏਕ ਦੇ…

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Q: 5. Let B = {(1,0), (0,1)} and B' = a.). b.) {(2, 2), (1,4)} be ordered bases for R² and let v = (-3,…

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Q: 2. Let M be the collection of all 2 × 2 real matrices. If define a b ^ - (**) EM A= C d |A| = and…

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Q: a) Given the following matrices a = -and c= nd 2. 3 and C = 2. i) AT C. i) 2(BC"). i) D if (2AB)" =…

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Q: Show that if the non-zero vectors s(1), s(2),..., s(m) are conjugate to a positive definite matrix…

A: We are given that the non-zero vectors s(1), s(2), ..., s(n) are conjugate to a positive definite…

Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

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Q: The graph shows the average cost of a barrel of crude oil for the years 1981 to 1990 in constant…

A: find explain below

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A: A rotational matrix, also known as a rotation matrix, is a special type of square matrix used to…

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

Q: Find the modulus = (ii) -1+3i 2-7 O Locate the numbers Z,+7 and Z,=Zz Vectorially when : + bi) ž,-…

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Q: 7) Find the Jacobian matrix at The print (1,2,1) of The Willowing Funchun: soudainish and Nidevorsh…

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Q: Mr Leon spent $60 on some apples, mangoes and pears in the ratio 3:5:2. The number of apples was…

A: Given Mr Leon spent $60 on some apples, mangoes and pears in the ratio 3:5:2. The number of apples…

Q: If there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multiple of one of the other…

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Q: Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C,…

A: Given statements, (i) In triple dot of vectors (A×B)·C=(B×A)·C where the vectors A,B, and C are not…

Q: Let A, BE MInn(R) be two square matrices. i) Explain what it means that the matrices A and B are…

A: All the sub parts are explained in details.