Put the following system in reduced row echelon form−3w+6x+2y+7z−2w+4x−3y−4z−w+2x−3y−5z=9=6=3

The system of equations you provided seems to be formatted incorrectly. However, I'll provide a general step-by-step guide on how to put a system of equations into reduced row echelon form.

1. Write the system of equations in augmented matrix form. For example, if you have the system of equations:

   2x + 3y - 4z = 1 -x + 2y + z = 2 3x - y + 2z = 3

   The augmented matrix would be:

   [2 3 -4 | 1] [-1 2 1 | 2] [3 -1 2 | 3]

2. Use row operations to create a leading 1 in the first row, first column. This can be done by swapping rows or dividing a row by a constant. For example, you could divide the first row by 2:

   [1 1.5 -2 | 0.5] [-1 2 1 | 2] [3 -1 2 | 3]

3. Use row operations to create zeros below the leading 1 in the first column. This can be done by adding or subtracting multiples of the first row from the other rows. For example, you could add the first row to the second row and subtract 3 times the first row from the third row:

   [1 1.5 -2 | 0.5] [0 3.5 -1 | 2.5] [0 -4.5 8 | 1.5]

4. Repeat steps 2 and 3 for the remaining rows and columns. The goal is to create a leading 1 in each row (moving from left to right) with zeros below and above it.

5. Once you have a matrix in row echelon form (with leading 1's moving from left to right and zeros below and above), you can further reduce it to reduced row echelon form by creating zeros above each leading 1. This can be done by adding or subtracting multiples of each row from the rows above it.

Remember, the exact operations will depend on the specific system of equations you're working with.