1. 2. 3. 4. Write the system as Ax = b and form the augmented matrix (Alb) ) Calculate det(A) and state whether the system has a unique solution AME ) Use Gaussian elimination to calculate REF of A and (Alb), state the rank of A and (Alb), and state how many solutions the system has. ) Use Gauss-Jordan elimination to calculate RREF of (AJI) and (Alb) to find A-1 and x, respectively

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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System 1:
System 2:
2x₁ + 2x₂x3 = -2
-x₁ = 1
2x₁ + 2x₂ + 2x3 = 4
x₁2x₂ - 2x3 = 6
-x₁ - x₂ +
2x₂23 = 0
-
= -4
Transcribed Image Text:System 1: System 2: 2x₁ + 2x₂x3 = -2 -x₁ = 1 2x₁ + 2x₂ + 2x3 = 4 x₁2x₂ - 2x3 = 6 -x₁ - x₂ + 2x₂23 = 0 - = -4
For the following systems of equations:
1. (
2.
3.
4.
5.
6.
) Write the system as Ax = b and form the augmented matrix (Alb)
) Calculate det(A) and state whether the system has a unique solution
) Use Gaussian elimination to calculate REF of A and (Alb), state the rank of A
and (Alb), and state how many solutions the system has.
) Use Gauss-Jordan elimination to calculate RREF of (AJI) and (Alb) to find A-¹
and x, respectively
) Perform LU decomposition and verify that LU = A
) Solve the system using your LU decomposition and verify your solution from
part 4.
Transcribed Image Text:For the following systems of equations: 1. ( 2. 3. 4. 5. 6. ) Write the system as Ax = b and form the augmented matrix (Alb) ) Calculate det(A) and state whether the system has a unique solution ) Use Gaussian elimination to calculate REF of A and (Alb), state the rank of A and (Alb), and state how many solutions the system has. ) Use Gauss-Jordan elimination to calculate RREF of (AJI) and (Alb) to find A-¹ and x, respectively ) Perform LU decomposition and verify that LU = A ) Solve the system using your LU decomposition and verify your solution from part 4.
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