# You Are Given The Original System Of Equations In An Augmented Matrix And Its 2858342

Hwk 2 Linear Systems of Equations
You are given the original system of equations in an augmented matrix and its
equivalent in reduced echelon form. For each question 1-3 answer the
following questions (a) Is the system of equations consistent or inconsistent;
(b) If the system is consistent, does it have a unique solution or many
solutions; (c) If the system has many solutions, give its general solution and
one particular solution.
1.
Augmented Matrix? Reduced Echelon form?
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0
1
3
0 0 0
0 1 13
1 0 30
3
1
1
5 12 6
2 5 5
1 2 4
2.
Augmented Matrix? Reduced Echelon form ?
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? 3
1
5
0 0 1
0 1 1
1 0 2
1
5
2
4 10 1
2 5 1
2 8 4
3.
Augmented Matrix? Reduced Echelon form?
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1
1/ 7
0
0 0 0
0 1 4 / 7
1 1 1
2
1
0
8 1 4
2 5 2
2 2 2
For each given system of linear equations:
? Place into an augmented matrix;
? Use elementary row operations to determine whether the system has/is:
1) An unique solution –if so state solution.
2) An undetermined system–state general solution and one
possible particular solution.
3) No solution–stop where you are using elementary row
operations and explain why the system is inconsistent with no
solution.
? Analyze the system: State the value of n, m, and n-r (number of free
variables) for each system.
4. Given a linear system of equations:
3 6 5 0
2 4 3 1
2 9
? ? ?
? ? ?
? ? ?
x y z
x y z
x y z
5. Given a linear system of equations
2 2 2 3
2 2 5 5
2 2 4 1
2 2 1
? ? ? ? ?
? ? ?
? ? ? ?
? ? ?
x y z
x y z
x y z
x y z
6. Given a homogeneous linear system of equations
3 6 0
4 8 5 0
2 3 0
? ? ?
? ? ?
? ? ?
x y z
x y z
x y z
7. Given a linear system of equations
2 3
2
1
? ?
? ?
? ? ?
y z
x z
x y z
8. Given a linear system of equations
5 5
2 7 8
1
? ? ? ? ?
? ? ?
? ? ?
x y z
x y z
x y z

Attachments: Hwk-2-Linear-….pdf 4.6/5

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