What is the elementary matrix corresponding to the following elementary row operation?
Table of Contents
What is the elementary matrix corresponding to the following elementary row operation?
In the table below, each row shows the current matrix and the elementary row operation to be applied to give the matrix in the next row….Introducing the left inverse of a square matrix.
| Matrix | Elementary row operation | Elementary matrix |
|---|---|---|
| [102−1001−1020−2] | R2↔R3 | M2=[100001010] |
How do you subtract rows from a matrix?
The number of rows and columns should be the same for the matrix subtraction. The subtraction of a matrix from itself results in a null matrix, that is, A – A = O. Subtraction of matrices is the addition of the negative of a matrix to another matrix, that is, A – B = A + (-B).
Can you subtract in elementary row operations?
2.2.1 Row operations We may therefore interchange any two rows without affecting the solution, giving thus another elementary row operation. We may add or subtract two rows after multiplying each by a chosen number. This constitutes another elementary row operation.
What does post multiplying a by an elementary matrix that is multiplying a by an elementary matrix on the right corresponds to?
Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form.
How do you solve elementary matrix operations?
There are three kinds of elementary matrix operations.
- Interchange two rows (or columns).
- Multiply each element in a row (or column) by a non-zero number.
- Multiply a row (or column) by a non-zero number and add the result to another row (or column).
Can we subtract two rows in a matrix?
As long as the dimensions of two matrices are the same, we can add and subtract them much like we add and subtract numbers. Let’s take a closer look!
What is elementary operations in Matrix?
The three basic elementary operations or transformation of a matrix are: Interchange of any two rows or two columns. Multiplication of row or column by a non-zero number. Multiplication of row or column by a non-zero number and add the result to the other row or column.