Given the initial augmented matrix
1 -1 0 2
3 -2 -2 3
-2 2 1 -3
RREF?
What is your question?
What does RREF stand for?
row reduced form
let U = {5,10,15,20,25,30,35,40} find 10,20
To find the Reduced Row Echelon Form (RREF) of a matrix, we perform a series of row operations until we reach a specific form. Here's how we can find the RREF of the given augmented matrix step-by-step:
Step 1: Swap rows if necessary to bring a non-zero value to the top-leftmost position (1st row, 1st column). In this case, the first row already starts with a non-zero value, so no need to swap.
1 -1 0 2
3 -2 -2 3
-2 2 1 -3
Step 2: Divide the first row by its leading non-zero coefficient (1) to make the leading coefficient equal to 1.
1 -1 0 2
3 -2 -2 3
-2 2 1 -3
Step 3: Use row operations to eliminate all values below the leading coefficient of the first row.
Multiply the first row by 3 and add it to the second row:
1 -1 0 2
0 1 -2 -3
-2 2 1 -3
Multiply the first row by -2 and add it to the third row:
1 -1 0 2
0 1 -2 -3
0 0 1 1
Step 4: Use row operations to eliminate all values above the leading coefficient of the third row.
Multiply the second row by 1 and add it to the first row:
1 0 -2 -1
0 1 -2 -3
0 0 1 1
Multiply the third row by 2 and add it to the first row:
1 0 0 1
0 1 -2 -3
0 0 1 1
Step 5: Finally, divide the second row by its leading non-zero coefficient to make it equal to 1.
1 0 0 1
0 1 -2 -3
0 0 1 1
This is the Reduced Row Echelon Form (RREF) of the original augmented matrix.