Can you multiply a matrix by (1/2) when doing Gaussian Elimination?

[diogenes2]

That's it, no problem or anything, I just wanted to know if this is possible.

 

[Steven G]

Will doing so change the solution to the system of equations?

Suppose a₁x₁+a₂x₂+...+a_nx_n=b. This has many solutions.
Now consider .5a₁x₁+.5a₂x₂+...+.5a_nx_n=.5b. Those this equation have the same set of solutions as the 1st equation.

Will this new equation have an affect on the solutions to the rest of the system?

 

[diogenes2]

Will doing so change the solution to the system of equations?

Suppose a₁x₁+a₂x₂+...+a_nx_n=b. This has many solutions.
Now consider .5a₁x₁+.5a₂x₂+...+.5a_nx_n=.5b. Those this equation have the same set of solutions as the 1st equation.

Will this new equation have an affect on the solutions to the rest of the system?

No, I guess not. Thank you! I was just wondering since my teacher said division was impossible.

 

[Steven G]

But division by x is just multiplication of 1/x. You can do division, just don't say that you are doing division!

 

[HallsofIvy]

Notice that Jomo was only talking about one equation. In terms of matrices that would be one row. In doing "Gaussian Elimination" on matrices there are three "row operations"
1) Swap two rows
2) Multiply an entire row by a number (or divide by a non-zero number).
3) Replace one row by itself plus a multiple of another row,

 

[Steven G]

Note that you can not multiply a row by 0.

I like to combine 2 and 3 from Prof Halls post and get:

You can replace a row with a (non zero) multiple of itself plus a multiply of another row.

 

[Steven G]

I just re-read the question. You want to know if you can multiply the whole matrix by 1/2. Yes, just apply the row operation that allow you to multiply a row by any non zero number to all three rows and let the multiplier be 1/2.