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I need help with Question #3 (d). I am not certain that it can be solved. -x+y+z=a x-y+z=b x+y-z=c

I need help with Question #3 (d). I am not certain that it can be solved. -x+y+z=a x-y+z=b x+y-z=c

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
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I need help with Question #3 (d). I am not certain that it can be solved. -x+y+z=a x-y+z=b x+y-z=c

RCISE 5.5 associated with a homogeneous system with a nonsingular matrix A. As a third pos we may have an infinite number of solutions. This eventuality is linked exclusively tem in which the equations are dependent (i.e., in which there are redundant equ Depending on whether the system is homogeneous, the trivial solution may or ma ** 0.0 included in the set of infinite number of solutions. Finally, in the case of an inc equation system, there exists no solution at all. From the point of view of a mode the most useful and desirable outcome is, of course, that of a unique, nontrivial 1. Use Cramer's rule to solve the following equation systems: (a) 3x1 - 2x2 = 6 2x₁ + x2 = 11 (b) x1 + 3x2 = -3 - X2 4x₁ - x2 = 12 7x1 - 3x2 = 4 2. For each of the equation systems in Prob. 1, find the inverse of the coefficie and get the solution by the formula x* = A-¹ d. 3. Use Cramer's rule to solve the following equation systems: (a) 8x1 - x2 = 16 (c) 4x+3y-2z=1 2x2 + 5x3 = 5 2x1 + 3x3 = 7 (b)x1+3x2+2x3 = 24 X₁ Chapter 5 Linear Models and Matrix Algebra (Continue + x3 = 6 8 (c) 8x17x2=9 X1 + X2 = 3 (d) 5x1 + 9x2 = 14 ZSS x + 2y = 6 + Z=4 (d) -x+y+z= a 3x x-y+z=b x+y=z=c 5x2 - X3 4. Show that Cramer's rule can be derived alternatively by the following pro tiply both sides of the first equation in the system Ax = d by the cofact then multiply both sides of the second equation by the cofactor |C2jl, etc newly obtained equations. Then assign the values 1, 2, ..., n to the inc sively, to get the solution values x₁, x2,...,x as shown in (5.17). n ion to Market and National-Income Mo can be solv
Transcribed Image Text:RCISE 5.5 associated with a homogeneous system with a nonsingular matrix A. As a third pos we may have an infinite number of solutions. This eventuality is linked exclusively tem in which the equations are dependent (i.e., in which there are redundant equ Depending on whether the system is homogeneous, the trivial solution may or ma ** 0.0 included in the set of infinite number of solutions. Finally, in the case of an inc equation system, there exists no solution at all. From the point of view of a mode the most useful and desirable outcome is, of course, that of a unique, nontrivial 1. Use Cramer's rule to solve the following equation systems: (a) 3x1 - 2x2 = 6 2x₁ + x2 = 11 (b) x1 + 3x2 = -3 - X2 4x₁ - x2 = 12 7x1 - 3x2 = 4 2. For each of the equation systems in Prob. 1, find the inverse of the coefficie and get the solution by the formula x* = A-¹ d. 3. Use Cramer's rule to solve the following equation systems: (a) 8x1 - x2 = 16 (c) 4x+3y-2z=1 2x2 + 5x3 = 5 2x1 + 3x3 = 7 (b)x1+3x2+2x3 = 24 X₁ Chapter 5 Linear Models and Matrix Algebra (Continue + x3 = 6 8 (c) 8x17x2=9 X1 + X2 = 3 (d) 5x1 + 9x2 = 14 ZSS x + 2y = 6 + Z=4 (d) -x+y+z= a 3x x-y+z=b x+y=z=c 5x2 - X3 4. Show that Cramer's rule can be derived alternatively by the following pro tiply both sides of the first equation in the system Ax = d by the cofact then multiply both sides of the second equation by the cofactor |C2jl, etc newly obtained equations. Then assign the values 1, 2, ..., n to the inc sively, to get the solution values x₁, x2,...,x as shown in (5.17). n ion to Market and National-Income Mo can be solv
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