Problem Set A1. Matrix A has dimension m x n and Matrix B has dimension s xt. Design conditions for m, n,s and t so that both matrix products AB and BA are defined.[2 marks]2. Two matrices are said to be identical, solve the unknowns in the following matrix equation:[3y 8 t²RIGHT410[18+ x18 y42 10][4 marks]

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Answered: 1. Matrix A has dimension m x n and…

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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4. Solve by Matrix Inversion. * For this number, solve using X = (A-1)B 2w – 2x + 3y + 4z = 33 3w – 5x – 7y + 3z = 11 4w + 3x – 4y – 5z = 3 5w + 4x + 6y – 2z = 45 1 Add file
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8. Find the inverse of each matrix below using elementary row operation 3 A = 1 a. 2 1 b. В - 3 1 1.
5. By using the matrix methods to solve the following linear system: x1 + x2 – x3 = 5, 3x1+ x2 – 2x3 = -4, -x1 + x2 – 2x3 = 3;
11. a. Find the inverse of the matrix if it exists: 5 15 56 -11 A = |-1 -4 -11 -41] -3 b. Solve the following system of equations, if possible: 5x1 + 15x2 + 56x3 -X1 - 3x2 - 11x3 = -7 -4x1 - 11x2 – 41x3 = -26 35 %3D 019 Chp 144 f12 ins ort sc 云
h 9 a ³1² ²₂/+1² 2+1² c d f Express Select one: This cannot be done for all values of a, b, c, d, e, f, g, h as there 8 of these but only 4 unknowns for the entries of the single matrix Oh+a b+e c+d d+fl Oh+2a g+b+e 3c 2d+2f Oh+a_g+b+e C d+f e as a single determinant in a manner that works for all a, b, c, d, e, f, g, h = R. We use | | to denote the determinant. None of the others apply
Matrix A has dimension m x n and Matrix B has dimension s x t. Design conditions for m, n,s and t so that both matrix products AB and BA are defined. Two matrices are said to be identical, solve the unknowns in the following matrix equation:
9. Consider the matrix 0 1 A 2 2 y -1 0 а. Write the equation det A = 0 in terms of x, y, and z. b. Explain why vị and v2, the first two columns of A, satisfy the equation you found in the previous part.
I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3
Consider the following linear equations: -5x + 5y +7z : 3 = 5 -5x+(21-k)y + 6z -5x + 5y + (11- k)z =k+11 a) X1 Suppose the above equation is expressed as Ax = b with x = X2 X3 equations in one matrix form as (A[b)= -5 5 7 124 -5 -5 Express the coefficients of the 3
Q1.Express the following system of equations in matrix forms and solves them by the elimination method (Gauss Jordan Method). i. x, + 2x, + x; = 2 3x, + x, – 2x3 = 1 4x, - 3х, — х, — 3 | 2x, + 4x, + 2xz = 4

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