Row Equivalent Matrices
3 important questions on Row Equivalent Matrices
What are Row Equivalent Matrices?
When we perform operations on rows in a matrix, we create a new matrix.
That matrix is in a sense equivalent to the original matrix.
A matrix can be said to be row equivalent if, by performing some row operations, we can turn one into the other.
That matrix is in a sense equivalent to the original matrix.
A matrix can be said to be row equivalent if, by performing some row operations, we can turn one into the other.
What is an augmented matrix?
Matrices can be used to solve for systems of equations.
When we do so, we 'transfer' all the elements in those equations into a matrix.
In order to distinguish between whats on one side of the equation (before the equal sign) and whats on the other side (after the equal sign), we draw a dotted line.
So the equations:
2x + 3y = 5
4x + 2y = 8
could be written as:
[ 2x + 3y : 5]
[ 4x + 2y : 8]
This is referred to as an augmented matrix.
When we do so, we 'transfer' all the elements in those equations into a matrix.
In order to distinguish between whats on one side of the equation (before the equal sign) and whats on the other side (after the equal sign), we draw a dotted line.
So the equations:
2x + 3y = 5
4x + 2y = 8
could be written as:
[ 2x + 3y : 5]
[ 4x + 2y : 8]
This is referred to as an augmented matrix.
What are the 3 things you have to remember to start simplifying a matrix?
a) You can interchange rows
b) You can multiply a row by a constant
c) You can add 1 row to another row
In your textbooks those things would be written as follows:
a) R1 <--> R2, meaning you are flipping Row 1 and Row 2.
b) 3R2 (sub2), meaning you multiply Row 2 by 3.
c) R2 + R3, you are adding Row 2 with Row 3.
b) You can multiply a row by a constant
c) You can add 1 row to another row
In your textbooks those things would be written as follows:
a) R1 <--> R2, meaning you are flipping Row 1 and Row 2.
b) 3R2 (sub2), meaning you multiply Row 2 by 3.
c) R2 + R3, you are adding Row 2 with Row 3.
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