What is M? system of linear equations

In summary, the conversation discusses how to obtain a matrix M from a given system of linear equations. The matrix consists of the coefficients of the unknowns in the equations. The conversation also mentions the use of row operations to simplify the matrix and obtain the desired solution.
  • #1
hawaiidude
41
0
what is M?
x1+x2=2x3+4x4=5
2x1+2x2=3x3+x4=3
3x1+3x2-4x3-2x4=1

why does M={ 1 1 -2 4 5 }
2 2 -3 1 3
3 3 -4 -2 1

i know how they got this but how do you get
~{ 1 1 -2 4 5 } { 1 1 0 -10 -9
0 0 1 -7- 7 ~~~ 0 0 1 -7 -7 ?? HOW?
0 0 2 -14 -14} 0 0 0 0 0
 
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  • #2
What is Q? What is P?

Come on, If you don't know enough to say WHAT the problem is, you are in real trouble!

I absolutely guarantee that the problem in your textbook doesn't say just "What is M?" without any explanation. You are given as system of linear equations and asked to find a MATRIX (which you happened to have called M- You could just as easily have called it "Fred" and asked "What is Fred?") consisting of the coefficients of the unknowns in the system of equations.

It looks to me like you haven't even copied the problem correctly. Did your equations really have those "=" in the middle? Do you really have 5 equations or 3? I'm betting 3.

Since you have 3 equations if 4 unknowns, you system will look like this when it is converted to "matrix" form:
[ a b c d][x1] [5]
[ e f g h][x2]= [3]
[ i j k l][x3] [1]
[x4]

Now multiply the matrices on the lefthand side. What do you get?
(You should have learned how to multiply matrices long ago if you are expected to do problems like this.) Compare the rows of the product matrix with the system of equation you are given. What do a, b, c, etc. have to be in order that the rows and equations are the same?
It should be obvious that the numbers in each row have to be exactly the coefficients in the equations. Once you have that, just add the "right hand side" of the equations as a fifth column.

Do you know what row operations are? Certainly if your textbook is doing problems like this "row operations" should be in the previous chapter or section. Look them up! Go to your instructor and throw yourself on his/her mercy!

Starting from [1 1 -2 4 5]
[2 2 3 1 3]
[3 3 -4 -2 1]
your objective is to arrive at [1 0 0 * *]
[0 1 0 * *]
[0 0 1 * *]
which would correspond to x1= * etc.

There are many different ways to do this. Just as you work with an entire equation at a time when solving equations, so you work with an entire row at a time (row operations). First: subtract twice the first row from the second: [ 1 1 -2 4 5 ]
[2-2(1) 2-2(1)3-2(-2) 1-2(4) 3-2(5)]
[3 3 -4 -2 1 ]
or [1 1 -2 4 5]
[0 0 7 -7 -7]
[3 3 -4 -2 -1]. The purpose was to get that "0" in the second row, first column.

Now subtract 3 time the first row from the third row to get a 0 in the first column of the third row: the result is
[1 1 -2 4 5]
[0 0 7 -7 -7]
[0 0 2 -14 -16]
Hmmm those "0"s in the second row look like trouble!
 
  • #3
o no sorry i got it...i was watching MIT's linear algebra lectures and i know...thanks.
 

1. What is a system of linear equations?

A system of linear equations is a group of equations that are interconnected and have the same set of variables. The solution to the system is a set of values for each variable that satisfies all of the equations in the system.

2. How is a system of linear equations solved?

A system of linear equations can be solved using various methods such as substitution, elimination, and graphing. These methods involve manipulating the equations to isolate a variable and solve for its value, and then using that value to solve for the other variables.

3. What is the purpose of using a system of linear equations?

A system of linear equations is used to model real-life situations and solve problems involving multiple variables. It allows us to find the relationships between different variables and determine how they affect each other.

4. Can a system of linear equations have more than one solution?

Yes, a system of linear equations can have one, infinite, or no solutions. One solution means that the equations intersect at one point, infinite solutions mean that the equations are the same, and no solution means that the equations are parallel and never intersect.

5. What is the role of "M" in a system of linear equations?

In a system of linear equations, "M" typically represents the slope of a line. It is used to determine the relationship between two variables and how they change in relation to each other. In some cases, "M" may also represent a constant value in the equation.

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