Complete augmented by row operations

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SUMMARY

The discussion focuses on achieving the reduced row-echelon form (RREF) of a matrix using row operations. The initial matrix is transformed through specific operations, including scaling rows and subtracting rows, leading to the final RREF of the matrix. The operations performed include dividing row 3 by 3 and row 4 by 2, followed by a row subtraction that simplifies the matrix to its canonical form. The final result confirms that the matrix is in reduced row-echelon form, demonstrating the effectiveness of systematic row operations.

PREREQUISITES
  • Understanding of matrix operations, specifically row operations
  • Familiarity with the concept of reduced row-echelon form (RREF)
  • Basic knowledge of linear algebra principles
  • Ability to perform arithmetic operations on matrices
NEXT STEPS
  • Study the properties of reduced row-echelon form in linear algebra
  • Learn about different methods for solving systems of linear equations
  • Explore matrix transformations and their applications in computational algorithms
  • Investigate software tools for matrix manipulation, such as MATLAB or NumPy
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as educators teaching matrix operations and their applications in various fields.

karush
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$\left[
\begin{array}{rrrr|r}
1& -5& 4& 0&0\\
0& 1& 0& 1&0\\
0& 0& 3& 0&0\\
0& 0& 0& 2&0
\end{array}\right] $
OK my first move on this is $r_3/3$ and $r_4/2$.
$\left[
\begin{array}{rrrr|r}
1& -5& 4& 0&0\\
0& 1& 0& 1&0\\
0& 0& 1& 0&0\\
0& 0& 0& 1&0
\end{array}\right]$
$r_2-r_4=r_2\quad$
doesn't this whole thing zero out?
 
Last edited:
Physics news on Phys.org
yep ... reduced row-echelon form is

$\begin{bmatrix}
1 & 0 & 0 & 0 &0\\
0 & 1 & 0 &0 &0 \\
0 & 0 & 1 & 0 &0 \\
0 & 0 & 0 & 1 & 0
\end{bmatrix}$
 

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