Reducing an augmented matrix by addition

[frctl]

This question comes from Elementary Linear Algebra
3x1 + x2 + x3 + x4 = 0
5x1 - x2 + x3 - x4 = 0
has the following augmented matrix:
3 1 1 1 = 0
5 -1 1 -1 = 0
In order to reduce can I add both equations?

 

[ksdhart2]

That's absolutely a valid method of obtaining the solution. The only caveat is that you should carefully read the instructions given. Even though the step is mathematically valid, it may not be "allowed" on this problem. That said, if you follow through with your suggested method, you'll end up with:

\(\displaystyle
(3x_1 + x_2 + x_3 + x_4) + (5x_1 - x_2 + x_3 - x_4) = 0 + 0 \\
8x_1 + 2x_3 = 0
\)
What next?

 

[frctl]

I'm not sure, can I solve this next by substitution?

 

[Dr.Peterson]

This question comes from Elementary Linear Algebra
3x1 + x2 + x3 + x4 = 0
5x1 - x2 + x3 - x4 = 0
has the following augmented matrix:
3 1 1 1 = 0
5 -1 1 -1 = 0
In order to reduce can I add both equations?

If you were told to solve by working with the matrix, then I assume you really mean, Can I add the rows?

Yes, you can add one row to another; but the real question is, will that help you toward your goal of reducing the matrix? That depends on what you choose to do next.

 

[frctl]

I arrived at my conclusions another way thanks to MarkFL

 

[Steven G]

This question comes from Elementary Linear Algebra
3x1 + x2 + x3 + x4 = 0
5x1 - x2 + x3 - x4 = 0
has the following augmented matrix:
3 1 1 1 = 0
5 -1 1 -1 = 0
In order to reduce can I add both equations?

You can get the 5 in row 2 to become 0 by computing 5R1 - 3R2

 

[Otis]

This question comes from Elementary Linear Algebra …

Hi frctl. You haven't actually posted a question. What exactly do the instructions say, for this exercise? REF? RREF? Something else? Please try to copy exercises word-for-word, as we ask in the Read Before Posting notice.

I arrived at my conclusions another way …

It's also good form to finish threads, by posting the answer, so that future readers can learn from the thread (and we can check it). Thanks!

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