Augmented Matrices: 0,7,3,1,alpha,-2

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In summary, The conversation discusses creating and row-reducing an augmented matrix to solve a system of linear equations. Alpha is a variable in the equations and the final matrix is not the inverse matrix. Alpha's value can be found by using row operations on the augmented matrix.
  • #1
Ry122
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How is this an augmented matrix?
Shouldn't 0 and 7 be 3 and 1 and alpha be -2?
http://users.on.net/~rohanlal/Untitled-1.jpg
 
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  • #2
The problem says associated augmented matrix.

Yes, construct the augmented matrix just as you say, then row-reduce to what they show. What is alpha?
 
  • #3
What is the matrix that is shown? Is it the inverse matrix?



What is alpha?

http://en.wikipedia.org/wiki/Alpha_(letter )
 
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  • #4
Ry122 said:
What is the matrix that is shown? Is it the inverse matrix?





http://en.wikipedia.org/wiki/Alpha_(letter )

:rofl:

I think he meant what is the alpha value when you transform your original augmented matrix to the final one (just do some row ops)
 
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  • #5
No, it's not the inverse matrix. That matrix is obtained when you express the 2 linear equations in the form of a matrix:

[tex]\left(\begin{array}{ccc}1&-2&1\\3&1&-2\end{array}\right)[/tex]

EDIT: I have no idea how to draw the vertical line in the matrix to represent an augmented matrix.

From here you just use row operations to get the matrix in the form given by the question. Alpha is then the value of whatever you have in entry row 2 column 3 of your reduced-row matrix
 

1. What is an augmented matrix?

An augmented matrix is a matrix that contains both the coefficients and the constants of a system of linear equations. It is typically used to solve systems of equations through the process of row reduction.

2. What do the numbers in this augmented matrix represent?

The numbers in this augmented matrix represent the coefficients and constants of a system of linear equations. The first three numbers in each row represent the coefficients of the variables, while the last number represents the constant term in the equation.

3. What does the "alpha" symbol represent in this augmented matrix?

The "alpha" symbol in this augmented matrix represents a variable or parameter. It can take on any value and is typically used to represent an unknown quantity in a system of equations.

4. How do you solve a system of equations using an augmented matrix?

To solve a system of equations using an augmented matrix, you can use the method of row reduction. This involves using elementary row operations to transform the augmented matrix into reduced row-echelon form, which will reveal the solutions to the system of equations.

5. Can an augmented matrix have more than one solution?

Yes, an augmented matrix can have more than one solution. Depending on the coefficients and constants in the matrix, the system of equations may have infinite solutions or no solutions at all. This can be determined by analyzing the reduced row-echelon form of the augmented matrix.

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