Put this matrix in Reduced Row Echelon Form. Make sure that you list the Elementary Row Operations that you use and show every step in order to solve this.
[ 1 2 1
-2 -3 1
3 5 0]
[1 0 -5
0 1 3
0 0 0]
give me a example of the hundred thousand digit of six-digit even numbers is 3 more than the thousand digit,which is twice the the ones digit.give at least four numbers that satisfy the given condition.
To put the given matrix in Reduced Row Echelon Form (RREF), we need to perform a sequence of Elementary Row Operations. Let's go through the steps:
Step 1: Perform Row Replacement
- Swap the first row with the second row to bring a leading 1 in the first row.
[ -2 -3 1
1 2 1
3 5 0]
Step 2: Perform Row Scaling
- Multiply the first row by -1/2 to make the leading coefficient in the first row equal to 1.
[ 1.0 3/2 -1/2
1 2 1
3 5 0]
Step 3: Perform Row Replacement
- Replace the second row by [second row - first row].
[ 1.0 3/2 -1/2
0 -1/2 3/2
3 5 0]
Step 4: Perform Row Replacement
- Replace the third row by [third row - 3*first row].
[ 1.0 3/2 -1/2
0 -1/2 3/2
0 -1/2 3/2]
Step 5: Perform Row Scaling
- Multiply the second row by -2 to make the leading coefficient in the second row equal to 1.
[ 1.0 3/2 -1/2
0 1 -3
0 -1/2 3/2]
Step 6: Perform Row Replacement
- Replace the third row by [third row + (1/2)*second row].
[ 1. 3/2 -1/2
0 1 -3
0 0 0]
Now, the matrix is in Reduced Row Echelon Form (RREF). The elementary row operations applied are:
1. Swap the first row with the second row.
2. Multiply the first row by -1/2.
3. Replace the second row by [second row - first row].
4. Replace the third row by [third row - 3*first row].
5. Multiply the second row by -2.
6. Replace the third row by [third row + (1/2)*second row].