Consider the following Gauss-Jordan reduction:1-9-3 0Find-9E₁= 0 10000 16.E₂ =0019-31 0A0E₁00 [10 07 [10 070 9 → 00 9001 41001 001 0B₂B₂₁AB₁AWrite A as a product A-E, ¹E, ¹E, ¹E of elementary matrices:B₂BAE₁=1 00000000 11 00010[10 070 1 0 1001EEEEA

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Answered: Consider the following Gauss-Jordan…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Let T: R³ → R² be given by 3x1 + 2x2 4.x2 – 5x3 T I2 and let L: R² → R³ be given by (:)- 6x1 + 12 -3.12 (a) Show that T and L are linear transformations by showing that they are given by matrix multiplication. (b) Find the standard matrix for the composition Lo T.
4. Use a computer to find: (a) Inverse of the Hilbert matrix: 1 1 /2 1/3 1/4 1/5 1/2 1/3 1/4 1/5 1/6 A = 1/3 1/4 1/5 1/6 1/7 1/4 1/5 1/6 1/7 1/8 1/5 1/6 1/7 1/8 1/9. (b) What is the condition number of A ? State which norm was used to find the condition number.
Matrices Use E(6) to find the inverse (if it exists) of each of the following matrices .
Consider the following Gauss-Jordan reduction: Find E₁ = -9 27 1-9 0 1 27-7-3=10001-7-300E₂A-9011 Write A as a product A = E¹E¹E¹E¹ of elementary matrices: 0 11 00-70 E,A >> 010-70 E₂,E,A 0 0 1 0 0 0 1 0 E₂ E₂ E, AO → HEACHEE+BEEHB E3 = 00 01 EEE₂E₁A = | E4= Consider the following Gauss-Jordan reduction Find 9 27 1 0 -7 0 -9 0 27 -7 1 0 A 1 -3 0 - 1 Write A as a product A=E, ¹E, ¹E, ¹E, of elementary matrices 7 00 E₁A 0 0 -7 0 001 100 E₂E₁A 0 0 100 ₂₂A n 00 010-I MESEMBEEHEEEHEEE == 001 EEEEA
Consider the following Gauss-Jordan reduction: 3 1 0 -3 1 2 1 0 2 0 1 0 = I 0 0 1 1 1 0 0 1 0 0 1 E‚A E,E,A E,E,E, A E,E,E2E¸A Find E1 = E2 = E3 E4 Write A as a product A = E,'E,'E, 'E,' of elementary matrices: | || 1 2 -3 1
Consider the following Gauss-Jordan reduction: [1 0 0] 8 0 8 0 1 0 E₁A Find E₁= [130] 3 0 8 0 8 0 0 1 A = 0 , E2 [1 [1 1 0 1 0 1 0 E₂E₁A 07 . Es Write A as a product A = E₁¹E¹E¹E¹ of elementary matrices: [100] 0 0 0 1 1 0 E₂E₂E₁A . E4 -888888888888 [1 07 0 1 0 0 0 1 E₁ E₂ E₂E₂ A = = I
4. Let E: P3 R2 be given by E (p(x)) = [P(2)] (a) Find a matrix that induces the transformation E. TH (b) Find a polynomial p(z) where E(p(x)) = [], or explain why this isn't possible. (c) Find a polynomial q(2) where E(q(z)) = [], or explain why this isn't possible. 8P (d) Find a nonzero polynomial r(z) where E(r(2)) = [] or explain why this isn't possible. (e) Describe the kernel of E. What is the dimension of the kernel? Find a basis for the kernel. (f) Describe the image of E. What is the dimension of the image? Find a basis for the image. (g) Is the transformation E one to one? Is it onto? Is it an isomorphism? Explain.
Consider the following Gauss-Jordan reduction: Find F₁ = 0 0 7 -7 0 1 - 0 B₂- 98 Write A as a product A E B E B of elementary matrices 1-1-61 →7 -7 0 0 0 BA 0 KA E₁ [10 01 100 101 - 0 01 E₁ A 001 BA
[101] Find the inverse of the matrix C = 01 1 using L2 1 4] cofactors. Show all your work.
Consider the following Gauss-Jordan reduction: Find E₁ = E₁ = ΤΟ 1 01 ΤΟ 1 0 50 1 07 [1 0 37 [1 0 01 103 ⠀⠀⠀⠀⠀ 0 0 1 Ę₂Ę₂ A [01 0 9 2 27 = 0 0 1 9 2 27 → 9 0 27 0 0 1 A 001 E₁A , E₂ = -1 1 Write A as a product A = E₁¹E₂¹E¹E¹ of elementary matrices: 0 1 0 0 0 1 E₂E¹₂E₂ A E3 = 010 0 0 1 E₁E₂E₂E₁ A = I
H 3

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Consider the following Gauss-Jordan reduction: Find E₁ = 0 0 -9 0 1 0 1 B₂ = 1 0 *-*-*-*-* 0 1 0 06- 6 E₂ = [100] Write A as a product A-E,E,'E,'E' of elementary matrices: ****-829999 E₁= 0900 900 10 1 0 1 Lo 0 0 0 [10 07 0 0 100

Consider the following Gauss-Jordan reduction: Find E₁ = 0 0 -9 0 1 0 1 B₂ = 1 0 --*-- 0 1 0 06- 6 E₂ = [100] Write A as a product A-E,E,'E,'E' of elementary matrices: ****-829999 E₁= 0900 900 10 1 0 1 Lo 0 0 0 [10 07 0 0 100