Write System of Equations 1

harpazo

harpazo

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The reduced row echelon form of a system of linear equations is given. Write a system of equations corresponding to the given matrix. Determine whether the system is consistent or inconsistent. If it is consistent find the solution.

How is done? I need the steps?

Below is the reduced row echelon form of a system of linear equations.

[1 0| -4]
[0 1| 0]
 
All you really need for this question is the concept of an augmented matrix -- the first couple paragraphs of this page, for example (or the last couple lines before Example 1).

Just reverse the process of creating an augmented matrix from a system of equations, to create the system corresponding to the matrix. You'll find that the system is very simple, and directly gives you the answer to the question.
 
harpazo said:
The reduced row echelon form of a system of linear equations is given. Write a system of equations corresponding to the given matrix. Determine whether the system is consistent or inconsistent. If it is consistent find the solution.

How is done? I need the steps?

Below is the reduced row echelon form of a system of linear equations.

[1 0| -4]
[0 1| 0]
Click to expand...
The system is consistent if it has a solution and inconsistent if it does not have a solution.

Assuming the variables from left to right are x and y, the the 1st line above says 1x+0y = -4 or x=-4
The 2nd line 0x + 1y =0 or y=0
 
Dr.Peterson said:
All you really need for this question is the concept of an augmented matrix -- the first couple paragraphs of this page, for example (or the last couple lines before Example 1).

Just reverse the process of creating an augmented matrix from a system of equations, to create the system corresponding to the matrix. You'll find that the system is very simple, and directly gives you the answer to the question.
Click to expand...

Thanks for the link.

So, if we go in reverse, the following should be the system of equations:

x + 0y = -4
0x + 0y = 0
 
Close. One of your zeros is probably a typo. (See Jomo's answer.)

So, is it consistent? What is the solution?
 
Jomo said:
The system is consistent if it has a solution and inconsistent if it does not have a solution.

Assuming the variables from left to right are x and y, the the 1st line above says 1x+0y = -4 or x=-4
The 2nd line 0x + 1y =0 or y=0
Click to expand...

Nicely done.
 
harpazo said:
Michael Sullivan's College Algebra 9th Edition Section 8.2.
Click to expand...
Okay. Now I'm wondering why Sullivan doesn't explain or show examples about any of the things asked for in this exercise (i.e., the correspondence between a given system of equations and the augmented coefficient matrix which models it, and how to determine whether a system is consistent or write solutions from RREF form).

Are you skipping ahead in the book? The last I heard, you were in the review section at the beginning of the text. I don't know whether you finished that review, but it seems like you're in Chapter 8 now. (What happened with Chapters 1 through 7?)

Have you read section 8.1?

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Otis said:
Okay. Now I'm wondering why Sullivan doesn't explain or show examples about any of the things asked for in this exercise (i.e., the correspondence between a given system of equations and the augmented coefficient matrix which models it, and how to determine whether a system is consistent or write solutions from RREF form).

Are you skipping ahead in the book? The last I heard, you were in the review section at the beginning of the text. I don't know whether you finished that review, but it seems like you're in Chapter 8 now. (What happened with Chapters 1 through 7?)

Have you read section 8.1?

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Click to expand...

Chapters 1 through 7 and section 8.1 has been covered.

I did read the text about properties per section including 8.1 and 8.2. However, the wording used by Sullivan, like most math and science books, is not too clear. Sullivan is super clear to you and other mathematicians here, but to someone like me who is reviewing material learned over 20 years ago, the jargon used is a bit fuzzy.
 
harpazo said:
Chapters 1 through 7 and section 8.1 [have] been covered …
Click to expand...
Great news! Do you feel ready to earn some extra money now, helping high school students with their word problems?

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Otis said:
Great news! Do you feel ready to earn some extra money now, helping high school students with their word problems?

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Click to expand...

I was a math tutor in the after school program for 8 years as a NYC Sub Teacher. I can help students in grades 1 through 10 but not ready for grades 11 and 12 in terms of math. I gotta review some trigonometry and precalculus material first.
 
Members here provide clear information. Is there any way for us to help you remember it?

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Otis said:
Members here provide clear information. Is there any way for us to help you remember it?

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Click to expand...

I learn best when

1. Tutors are patient with my ignorance replies to comments made by others

2. When steps are given

For example:

Solve 3x = 15 - 5 for x.

STEP:

A. Subtract 5 from 15 on the right side.

B. We now have 3x = 10.

C. Divide both sides by the coefficient of x, which is 3 in this case. This leads to x = 10/3.

D. Check your work by plugging x = 10/3 in the original problem.

E. After doing step D, you should get the same answer on both sides of the linear equation. Step E will prove your answer to be right.

This is what I need. . .STEPS.
 
Actually, people who memorize specific steps don't do very well in math, at least when they are faced with a problem even slightly different from the one they were taught. That's why we try to focus on engaging a student to think for themselves, rather than telling them what to think.

The way to solve your equation is not to follow those steps, but to know what kinds of things you can do (such as combining like terms or adding the same quantity to both sides), and to focus on the goal (getting x alone). Then they can decide what steps will work best here.

And the way to learn to think for yourself is not to watch someone else do it, but to actually think for yourself -- including making mistakes, catching them, and then saying, "I'll never do that again". That is much more memorable!

I'll add that my own memory has never been great; so these ideas are very important to me, personally. If I depended on memorizing a list of steps, I'd be in big trouble. On the other hand, I'll admit that generalized "steps" can be helpful. For example, I recommend a three-step procedure for algebra: simplify, solve, check. But that's more a lifestyle than a list.
 
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