Use the matrices P and D to construct a spectral decomposition of A= PDP-¹ A = -8 -4 4 -4 - 10 0 P=[U₁ 4 0-6 4₂ 5 U3] = 2 W|N W|NW|→ -13 ~/m W|N 2 3 3 WIN ب ابن 2 1 ف ال 3 ē 11 -2 O O 0 0 -8 0 0-14 T T T A spectral decomposition of A is A = (u₁u₁ + ¹₂u² + ( uzu?, where u₁u} = ₁ u₂u² = ₁ and u₂u² = - (Simplify your answers.)

Q: iv) Find a basis for ker(T). 1o lamsd zied v) Determine the dimension of the ker(T). vi) Find a…

A: Given Transformation convert to the matrix T(w)= 3-6  2-2 4  1 1-2-1-1 2  2 Transform the matrix to…

Q: Let L: R2 R² be defined by L such that [L(u)]s, = P[u] B₁₂" P = +4[X₂]-[xx+³x³] · ↓ 1 ›-{[8]· [;)]}…

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Q: "he determinant of the matrix 1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 A = |1 2 3 4 5 6 7…

A: Here since the columns of matrix A is linearly dependent

Q: (a) Construct the 3 × 3 matrices A₁ and A₂ associated to the linear transfor- mations L₁ and L2,…

A: (a)Two Linear transformations are mentioned:.Thus the matrix for the transformation  is given by and…

Q: 8z Compute the inverse z-transforms of z²-6z+25

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Q: The linear transformation_T:R³ OK² is represented. by the matrix [T]8= 1 20 where B= 012 and B' = 二…

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Q: Suppose T: M2,2→P3 is a linear transformation. Let A, B, and C be the matrices given below, and…

A: Suppose T:M2,2→P3 is a linear transformation. Let A, B and C be the matrices given below, and…

Q: T:R2 x → M2x2(R) is a linear transformation. If :) 2 1 3 (1 2 T(1+ x + x²) = 3 ,T(1+ 2x + x?): 4…

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Q: 4. Consider two 3 × 3 matrices A and B with det(A) = -2 and det(B) = -1. Let T(*) = Až be a linear…

A: solution :-

Q: 2. Find the 3 x 3 matrix representation of the 2D reflection transformation about line 2y + x – 4 =…

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Q: Let T be a linear transformation from M2,2 into M2,2 such that ([D-[-] ([:D)-[; ²] ([: :)) - [1 ²];…

A: Given :T1000=1-102T0100=0211T0010=1201T0001=3-110

Q: Find an LU decomposition of 7-779 A= -1 -1 11 7 1-3 -1 21 -1 17 15

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Q: 3 2-1 0 -3 4 26-2 Compute the LU decomposition for A- 6 4-2 3 0 0 0-6-10

A: The LU decomposition of a matrix A is writing the matrix A as the product of matrices L and U where…

Q: Complete the matrix representation for the linear transformation T : P2 → P2 given by T(ax? + bx +…

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Q: The linear transformation T:P2 → P2 is defined as T(ax^2 +bx+c) = bx^2 +ax−3c. (a) Compute T (3x^2…

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Q: Let T: R² → R³ and S: R³ → R² be two linear transformations. Suppose the matrix of T is 21 -1 and…

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Q: why no matrix exists for one-to-one linear transformation from R^4 to R^3

A: Given: We have to prove no matrix exists for one-to-one linear transformation from R4 to R3.

Q: Describe in words the linear transformations R2 → R2 that have the matrix representation AT,…

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Q: Let T: R³ → R² be a linear transformation. If it is known that Img (T) = CL {(_^), (8)}, t then…

A: Given  T:R^3 to R^2.    ....(1) And img(T)=CL{(4,-4),8,-8)} ...(2) By (1), T is 2*3 matrix  As we…

Q: Xị – 5x2 – 4x3 3x2 + 4x3 • X1 - for all a E R³. X2 T(7) %3D %3| -2x1 + 6x2 X3

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Q: 1. (a) Define: invertible linear transformation. (b) T: (7₁,72) → (67₁ - 872,-57₁ +77₂) is a linear…

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Q: Let 0 3 0 1 1 2 2 1 A = -1 B : 0 1 1 2 0 1 -2 Compute det(AB), det(A-'B-!) and det(2A) where 2A…

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Q: Draw a transformation diagram for v = (3/5)c, with the numbers 1, 2, and 3 (in meters) on the…

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Q: Suppose T is a linear transformation such that -5 6 -31 [3] 1 T-13 = -3 T-8 = 1 and T-2 0 0 5 6 1…

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Q: 105 find a matrin A = singulay decomposition of

A: The objective is to find singular decomposition of the matrix A=110110 Now, AT=101110 Let,…

Q: Verify that A = U£VT,

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Q: linear transformation A maps P(1,0) to P’(-2,-4) and Q(0,1) to Q’(4,1). Find (i) The matrix A (ii)…

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Q: 5. Use spectral decomposition to orthogonally diagonalize the matrix A = 5 10 {]. 5

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Q: 9. What is the rank of L defined in the previous item? (a) 1 (b) 2 (c) 3

A: Given matrix is A = 125202423030

Q: 3. With the transformation matrix (A) given by (4.20), explicitly verify that 3 Σaijaik = δjk, i=1…

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Q: [1 The columns of 3 = 0 O Suppose that T is a linear transformation from R³ into R² such that T(e₁)…

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Q: Obtain the Hartley transformation matrix for N = 4.

A: As per the question we have to find the Hartley transform matrix for N = 4 For that we will start…

Q: Find Canonical Transformation of the following equation 4 ury + 4 uyy = 0 None {e = y- } 1 ; n= y -…

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Q: The standard matrix of the transformation I defined by T(x,,X2,X3)= (x, +2x2,-X3, 4x, -x3) 1 1 2 0…

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Q: Let S P₂ P₂ be the linear transformation where S(x) = -12x - 30 and S(1) = 5x + 13. 0 Suppose Mg(S)…

A: Let,      B = {x + a, x + b}  Now,        S(x + a) = S(x) + aS(1)                       = -12x - 30…

Q: transformation_of the following equation 3 urr +10 ury +3 Uyy } 1 y+5¢ ; 7 = y+3x None } 7=y-3z }

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Q: A 3 T = (l:))-I:1. "(;)) T Consider a linear transformation T from R³ to R2 for which 0 8 (A) - (A)…

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