Question

As Tia solved the system of equations below, she transformed matrices at different steps during the process.

mc015-1.jpg

She noted the following matrices.

I
II
III
IV
mc015-2.jpg mc015-3.jpg mc015-4.jpg mc015-5.jpg

In which order should the matrices be arranged when solving the system from start to finish?
I, IV, III, II
II, III, IV, I
II, IV, I, III
IV, II, III, I

Answer 1

I can’t see the images you attached. Could you either

- paste the four augmented matrices here as text (for example: [[1,2,-1|3],[0,1,4|5],...]) or
- type each matrix row-by-row, or
- describe each matrix (the pivot positions, any rows of zeros, any rows with a single nonzero entry on the right, etc.)?

If you want to decide the order yourself, here are quick identification tips you can use:

- The starting (original) matrix usually has no leading 1s forced yet and will often have nonzero entries below the first pivot.
- After the first elimination step you should see zeros below the first pivot in its column (but there may still be nonzero entries above that pivot).
- After further elimination you’ll have zeros below pivots in the first and second pivot columns; if it’s in row echelon form pivot entries need not be 1 yet.
- The final matrix (reduced row echelon form) has 1s as pivot entries and zeros in every other position of a pivot column (so each pivot is the only nonzero in its column).
- If one row is [0 0 ... 0 | nonzero] that indicates the system is inconsistent — that matrix would appear after elimination yields a contradiction.

Paste or describe the matrices and I’ll put them in the correct order.