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innightmare
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I am having problems with understanding the whole concept/how to compute the row-reduced echelon form.
Can someone please help me? Thanks
Can someone please help me? Thanks
An upper triangular matrix is a matrix that has only zeros below the "main diagonal".innightmare said:The book that i have doesn't give examples nor is it clear about the upper triangular matrix. Can you PLEASE explain what's an upper triangular matrix?
A row-reduced echelon form (RREF) is a specific form of a matrix where the leading coefficient (first non-zero number) of each row is a 1, and all other numbers in the same column are 0. This form is useful for solving systems of linear equations and performing other operations on matrices.
To transform a matrix into RREF, we use elementary row operations such as multiplying a row by a non-zero number, swapping two rows, or adding a multiple of one row to another. These operations do not change the solution to the system of equations represented by the matrix.
RREF is useful for solving systems of linear equations because it allows for easier identification of the number of solutions (one, infinite, or none) and the values of the variables. It also simplifies matrix operations and makes it easier to find the inverse of a matrix.
Not all matrices can be transformed into RREF. For example, matrices with all zero rows cannot be transformed into RREF. Additionally, some matrices may require more complex operations to reach RREF, while others may not have a unique RREF.
RREF is used in various fields of science, such as engineering, physics, and computer science, to solve systems of linear equations and perform matrix operations. It is also used in data analysis and machine learning to simplify and manipulate large datasets.