↓[19 -30 -68 -237]9-12-304 -9↓A matrix A= 9 -12Calculate a basis for Nul-A:-114 reduces to-17 -48-100-3 -3-30002 31-3-3]

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Answered: 19 -30 -68 A-matrix A= 9 -12 -30 4 -9…

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 1 Which of the following is the matrix C that satisfies the equality (CT- 412) 5 3 (:) -1 3 (a) 2 -5 -2 (b) -3 1 (:) 7 -5 (c) 6 -5 (d) -1 -5 5 (e) -6 6 1.
Consider the below 3 equations, U₁ = C₁-C₂ + C3 U₁= C₁ + (0*C₂)+ (0*C3) = C1 U₁ = C1 + C₂ + C3 In Matrix form, 1 -1 1] 10 1 Solve to get the below final form, C₁ 5 C3 || C₁ U₁ 0₁²₂}=- u, 1||C3 U₂ 12 U₁ (u₁-2u, +Ug) ¹ (Ug-u₁)
aliil JlaSl aL find (a) AB (b) BA (if they are defined) for the following matrixes 2 1 0-1 0 -3 4 1 6 4 0 2 8-1 7 6 -21 5 (a) 8 -3 19 2 7 (b) Not defined 1 -12 5 (a) 4 -2 19 2 7 3 3 -4 (b ) 10 16 26 46
I A 3x5 matrix B= [b₁ b₂ b₂ by b₂] 10 301 has RREF R= 4] 01-204 00011 A. Find a nontrival relation C₁ b₂ + C₂ b ₂ + C₂ b ₂ + Cyby +Cgbg=0 B. Given b₁ = [2]. b₂ ² [5] by [ 3- by = [ o ] C. what is basis for Col(B)? find bs
7.Find the inverse of the given matrix [1 A = 1 [1 a) A-¹ = b)A-¹ c) A-¹ d) A- = || = -1 1] 1 1 2 4 = 1 6 1 6 116 16 1 0 1 2 -3 1 26 -2 [1 1 -1 3 6 3 -3 -3 1 -3 2 30 1 -1 5 [1 6 1] 1 4] NON 1 6 4.
8. Transform the augmented matrix M to triangular matrix. -1 -1 4 -1 (A) 0 0.67 4.33 3.33 (B) 0 0.67 -4.33 3.33 Riz Ri-(RX 21) 0 6.50 12.0 -1 -1 0₁-6.50 12.0 -1 -1 (C) 0 -0.67 4.33 (D) 0 -0.67 -4.33-3.33] (3-4-14 છે. 0 lo 0 -6.50 -12.01 201² + 2001 2x142 1 300309 -3.33 6.50 -12.0 Els M=4 -2 3 2 L2 1 -5 -1
0 1 12 -7 9 -3 -3 invertible matrix P satisfying A = P-¹BP. Show that A P-1 = = 0 1- and B = -19 24 -16] -22 30 -18 27 -22 are similar matrices by finding an -21, P =
[ 2n + 1 7][ 6 4) Determine the following matrix product, En +1 33n – 1 n + 1] 2 in terms of n. 5) Let n be a positive integer such that 7| (82-1). Prove that 7| (8-1 - 1). (Hint: Rewrite 8n*1 -1, where a portion of the expression is 8 times 8" - 1.)
5 15. Let A be the matrix -3 1 (a) Compute A-1. (b) Use part (a) to find the unique solution to the matrix equation AX
Q) Answer the following. (50 Marks) (a) Determine the inverse of the matris - A- S 3 51 b) Find the Transpose of a matrix - A-(2 5 1 A- i3 -24 24 Q2) Answer the folloning --(50 Marko) 1- limr'n 2- lim 3y+2 - lim lim 4-

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19 -30 -68 A-matrix A= 9 -12 -30 4 -9 -17 alculate-a-basis-for-Nul-A:↓ -237] -114 reduces to 0 res-to- -48 0 23 -3 -3 -3↓↓ 0 -3] 00