Dick said:What about:
1 a
0 0
where a is nonzero?
I copy and pasted the instructions. I think all I need to do is list them, but I'll check with my prof tomorrow.christoff said:I would consider "describing" all 2x2 RREF matrices as simply listing them, so I would think that you are done.
Could you quote the problem exactly?
Dick said:What about:
1 a
0 0
where a is nonzero and not 1?
pyroknife said:Hey, I copy and pasted the instructions. I think all I need to do is list them, but I'll check with my prof tomorrow. ! DAng it. Would've never thought of that one. Using that matrix means there are infinite matrices of that form. Or I can classify it as one form with a variable.
Thanks a bunch for the help guys.Dick said:Sure, list it like that. Then you can drop:
1 1
0 0
It's a special case.
pyroknife said:Thanks a bunch for the help guys.
What do you mean by special case?
Or could I also drop
1 0
0 0
and define a is any number?
A 2x2 matrix is a rectangular array of numbers or variables arranged in two rows and two columns. It is commonly used in linear algebra to represent systems of linear equations.
RREF stands for Reduced Row Echelon Form. It is one of the standard forms for representing a matrix and it has several useful properties for solving systems of linear equations.
To find the RREF of a 2x2 matrix, you can use Gaussian elimination, which involves performing elementary row operations on the matrix until it is in its reduced form. This includes operations such as swapping rows, multiplying a row by a constant, and adding one row to another.
A 2x2 RREF matrix has several properties that make it useful for solving systems of linear equations. These include having a leading 1 in each row, having zeros below each leading 1, and having the leading 1s occur in columns to the right of previous leading 1s. Additionally, the last row of the matrix will contain either all zeros or all zeros except for the last entry, which will be a 1.
RREF matrices can be used to solve systems of linear equations by representing the equations in matrix form and using Gaussian elimination to reduce the matrix to its RREF form. This allows for a systematic way to solve the equations and find the values of the variables in the system.