[1 2 31 Q2: Consider A = 2 4 5 l1 3 4] a) Check if the A has LU decomposition b) Find an LU decomposition c) Then solve X1 + 2x2 + 3x3 = 4 2х1 + 4x, + 5х3 — 6 X1 + 3x2 + 4x3 = 2

Q: 7. Which of the following is the LU decomposition of 4 -2 3? 8. -2 1 0 2 1 -2 2 1/2 2 -2 1 -4 1 2,…

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Q: Use the divergence theorem to evaluate || F•ndS where F(x,y,z)=xi+ yj+zk . n is the outer unit…

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Q: 3. Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the…

A: 3. Describe all solutions of  in parametric vector form, where A is row equivalent to the given…

Q: Which of the following is the function z in terms of the variable x that needs to be converted in…

A: The least square regression technique uses a dataset to determine a linear equation, such that the…

Q: If L and U are invertible, then (LU) – Find A from the given LU factorization: 9 -27 7-14 96 = -63…

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Q: 4. Given A=| 3 5| Find a) the characteristic roots b) the characteristic vectors c) Check the…

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Q: Find the singular value decomposition R= UEV• for the matriz 2 2 R=|3 4 4 5 5 6

A: We are given that R=1122344556. Now, RRT=247911481418227142532399183241501122395061. Now, finding…

Q: Explain the relationship between the statistical GM: Y, = Bo + B] x; + u;, teN and the estimated…

A: and the estimated orthogonal decomposition:

Q: Find the orthogonal complement to the row space of A and its dimen- sion.

A: Given , A = 125213037 Then , the now-space is span of                   (1,2,5)  ,  (2,1,3)  and…

Q: The two open disks B((1,2);2) and B((-2,1);1) has intersection. True or False

A: The two open disks B1,2: 2 and B-2,1: 1 We have to find there is any intersection between these…

Q: Find the projection ofv onto u

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Q: In this question, we will find the reduced singular value expansion of the matrix 2. 1. A = 1

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Q: Find a singular value decomposition (SVD) for A = Verify that A = UEVT.

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Q: Exercise 1.12 Let M (23). Compute two different simplified row reduced forms of M. Conclude that the…

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Q: Let p(x) = a0 + azx + azx and q(x) = bo + bịx + br? be vectors in P2 with (p, a) = agbo + azb; +…

A: The given vectors are v1=-1+x2 and v2=-1+x. By the given definition of inner product, for…

Q: Given that A is transformed into U by the elementary row operations below, find L. A = L= -5 8 10…

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Q: 18 f1. are the corresponding Christoffel symbols and are components of two symmetric covariant…

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Q: Stable molecules form when atoms arrange in a way to exert equal force on each other. One such…

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Q: Let u=-3i+3j+2k and v=i+j+3k and find u . v, that is, the cross product of u and v

A: Let  u→ and v→ be the two vectors .   i.e, u→=u1i^ +u2j^+u3k^  and  v→=v1i^+v2j^ +v3k^ Dot product…

Q: a) Find the basis for the solution space of I1 +a2 - r3 = 0, -2r1 - 12 + 5r3 = 0, -11 + 4r3 = 0 %3D…

A: (a) given system of linear equation x1+x2-x3=0-2x1-x2+5x3=0-x1+4x3=0 to find - basis for solution…

Q: [1 2 31 Q2: Consider A = |2 4 5 li 3 4] a) Check if the A has LU decomposition b) Find an LU…

A: An LU decomposition of a matrix A is the product of a lower triangular matrix and an upper…

Q: 2a) Find the area of triangle PQR where P is (4, 2, 5), Q is (3, -1, 6) and R is (1, 4, 2) [1 2 31…

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Q: (c) Write C(A) as the span of a set of linearly independent vectors. (d) Write N(A) as the span of a…

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Q: Suppose that a parametrization for the solution set to the equation Ax = b is -2 -3 + x2 + x3 8.…

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Q: Verify that A = U£VT,

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Q: Determine the LU decomposition (without pivoting) of the following: 2 2 1 - 2 1 4 91 00 8 O 1 0 0 L=…

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Q: Suppose A is not diagonalizable. If the characteristic equation of A is: -λ +2^² - 2³ = 0 then dim…

A: Given :-  A is not diagonalizable. And Characterstics equation.  Topic :- Matrix.

Q: V has bases B = (v1, v2, v3) and B' = (w1,w2, W3). If wi vị + 2v2 + 4v3, wz = 2v1 + 5v2 + 6v3, wz =…

A: Given that, B=(v1,v2,v3),B'=(w1,w2,w3) Given that,…

Q: Fend the general solution of each of the hamo genous lneor Systems using vector-matrix method. dx dt

A: Characteristics equation of A  is: ch(A)=λ2-2λ+5 Determine the value of λ. λ=2±4-202=2±4i2=1±2i…

Q: 6. Prove that the Rotation Matrix R corresponding to quaternion q = (a, b, c, d) is given by 1. R=…

A: Hint:    Consider a 3×3  matrix      a00a01a02a10a11a12a20a21a22