[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: Q1) Express in matrix notation: x' = (cos 2t) x y' = x – (sin 2t)y +1 z' = 1- x + 3y

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Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2k 2k +2 3k +1 3k +4 k=1 2 а) 3 b) 0 c) 6 1 d) e) Diverges. ||

A: Given series is  ∑k=1∞2k3k+1-2k+23k+4 where ak=2k3k+1-2k+23k+4 the above series is telescopic…

Q: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

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Q: Q.2:0Find the inverse the matrin A = -1 8 to (I A""). by converting Cii) P leas (A! 2) Comment on…

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Q: 4. Define Let T: M2x2 (R) → P2(R) by T (a b) = (a + b) + (2d) x + ba². c d B = {69). C )·(9)· (9)}…

A: We will find the matrix with respect to the basis.

Q: O 2 2] B = 0 2 0 0 0 2 TRUE or FALSE: B is diagonalizable.

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

A: and the estimated orthogonal decomposition:

Q: -1 21 1 2 Show that A = 2 2. is diagonalizable by finding P and D such that P-'AP=D for a diagonal…

A: The matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

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 the projection ofv onto u

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Q: Find the cross product u x 7 where u = 2i -3j +k and = (7, - 3, 4). ü xü= Check Answer

A: We have u→=2i-3j+kor u→=2, -3, 1Alsov→=7, -3, 4

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

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

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

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Q: 2 -3" A = 2 –1 4 4 3 -2

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Q: Q1/ Consider the following equation Uxx +Uxy -2uy +1=0 xX, 1) Determine the type of the equation. 2)…

A: We use classification of second order PDE then find the canonical form.

Q: Compute the following cross products: (а) ј x (3і — ј + 2k); (b) (1,2, 3) х (3, 2, 1); (с) (і — ј+…

A: Let a Vector A→=xi+yj+zk and B→=ai+bj+ck then Cross Product between two vectors A→ and B→ is given…

Q: Find the roots of the following equations, assigning the results to ra, rb, and rc respectively a)…

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Q: Section 1: K/U Multiple Choice: [3 Marks] 1. Derivative of y = 14 is: a) 0 b) 1 2. Derivative of…

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Q: Find J2z Әх у of z = x3 + 5x² у + 6

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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: 4. Let p(x) = a + a₁x + a₂x² and q(x) = bo + b₁x + b₂x² be vectors in P₂ with: (p, q) = aobo + a1b₁…

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Q: Find the matrin of linear 2 22

A: The domain of the given transformation is R3:   To find the matrix of the linear transformation,…

Q: Q1/ Consider the following equation Uxx +Ury - 2u vy +1=0 1) Determine the type of the equation. 2)…

A: Given PDE is uxx+uxy-2uyy+1=0 comparing with Auxx+Buxy+Cuyy+f=0 We have   So…

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: (8 (10 pay x/x = (x+x)= xpe (1)3-x 21-AIBALI only one

A: As per bartlby guidelines we can answer only first question and rest can be reposted

Q: ) Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 %3D Write out Q(x) in terms of z1,…

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Q: Use the inner product (A,B) = 2a11b11 + a21b21 + a12b12 + 2a22b22 to find (A, B) for 0 A - [27][221]…

A: Given A = 1-124,   B = 01-20

Q: [Q6] (Section 1.4, Linear Algebra Review; related to Theorem 1.4.4) Let M e RmXn, and assume that M…

A: The matrix A is symmetric positive definite.

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: gona u = 2i – 3 j+5k v= 4i -9j-7k

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Q: 2i -1+iy -2 + i) are linearly independent over C ? -1+ 3i)

A: If rank is less than 2 we will get a matrix which is linearly dependent.