Consider the following system of equations.x1 + x2 + x3 = b1x1 − x2 + x3 = b2x1 − 2x2 − x3 = b3 (a) Write the system of equations as a matrix equation. x1 x2x3 = b1 b2b3(b) Solve the system of equations by using the inverse of the coefficient matrix.(i) where b1 = 5, b2 = −5, b3 = 0(x1, x2, x3) = (ii) where b1 = 2, b2 = 5, b3 = −3(x1, x2, x3) =

Given: x1+x2+x3=b1 ..1x1-x2+x3=b2…

Answered: Consider the following system of…

Consider the following system of equations. x1 + x2 + x3 = b1 x1 − x2 + x3 = b2 x1 − 2x2 − x3 = b3 (a) Write the system of equations as a matrix equation. x1 x2 x3 = b1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.CM: Cumulative Review

Problem 6CM

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Question

Consider the following system of equations.

x₁	+	x₂	+	x₃	=	b₁
x₁	−	x₂	+	x₃	=	b₂
x₁	−	2x₂	−	x₃	=	b₃

(a) Write the system of equations as a matrix equation.

x₁

x₂

x₃

b₁

b₂

b₃

(b) Solve the system of equations by using the inverse of the coefficient matrix.

(i) where

b₁ = 5, b₂ = −5, b₃ = 0

(x₁, x₂, x₃) =

(ii) where

b₁ = 2, b₂ = 5, b₃ = −3

(x₁, x₂, x₃) =

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