Question

[1 2 -1 0]
[-1 1 0 5]
[1 0 3 6]

help me solve, w/o doing errors.
I did those 2 yrs ago, but don't remember.......

Answer 1

[1 2 -1 0]
[-1 1 0 5]
[1 0 3 6]

[1 2 -1 0]
[0 3 -1 5]
[1 0 3 6]

[1 2 -1 0]
[0 3 -1 5]
[0 -2 4 6]

Doing some changes to the 1st, 2nd and 3rd rows of the matrix.
[3 6 -3 0]
[0 6 -2 10]
[0 -6 12 18]

(two steps at once)

[1 0 1 -10]
[0 6 -2 10]
[0 0 10 28]

[10 0 10 -100]
[0 6 -2 10]
[0 0 10 28]

[10 0 0 -128]
[0 6 -2 10]
[0 0 10 28]

[10 0 0 -128]
[0 30 -10 50]
[0 0 10 28]

[10 0 0 -128]
[0 30 0 78]
[0 0 10 28]

[1 0 0 -12.8]
[0 1 0 2.9]
[0 0 1 2.8]

I got weird answers, are they correct? Can someone show me where is my mistake?

Answer 2

Please CHECK my work and explain the mistake(s)!

Answer 3

You made a mistake at "2 steps at once." Should go from
\[\left[\begin{matrix}3 & 6 & -3 & 0 \\ 0 & 6 & -2 & 10\ \\ 0 & -6 & 12 & 18 \end{matrix}\right] \begin{matrix}R_1 & \\ R_2 \\ R_3 & \end{matrix}\ \]
\[ \left[ \begin{matrix} 3 & 0 & -1 & -10 \\ 0 & 6 & -2 & 10\ \\ 0 & 0 & 10 & 28 \end{matrix} \right] \begin{matrix} R'_1 = & R_1 - R_2 & \\ R'_2 = & R_2 \ \\ R'_3 = & R_2 + R_3 & \end{matrix}\ \]

Answer 4

the z is right though,

Answer 5

The x isn't though

Answer 6

Should be 3x - z = -10 in the first row

you had x - z = -10

Answer 7

If you add a checksum column it'll help prevent mistakes like that. Add one more column to the end of each row and put the sum of the row in it, then do operations the same on that as you would normally. If you did the operations correctly, the row should add up to the checksum column \[\left[\begin{matrix}3 & 6&-3&0 &| \ \ 6\\ 0 & 6&-2&10 &|14 \\ 0 & -6 & 12 & 18 & |24\end{matrix}\right]\]

\[ \left[\begin{matrix} 3 & 0&-1&-10 &|-8\\ 0 & 6&-2&10 &| \ \ 14 \\ 0 & 0 & 10 & 28 & | \ \ 28 \end{matrix} \right] \]

first checksum:
3 - 1 - 10 = -8 = 6 - 14 YAY!

second
6 - 2 + 10 = 14 = 14 YAY!

third
10 + 28 = 38 = 14 + 24 YAY!

Answer 8

The Z is right though, yes :)

Answer 9

~~~ also, the last checksum of row 3 should be 38, not 28

\[ \left[\begin{matrix} 3 & 0&-1&-10 &|-8\\ 0 & 6&-2&10 &| \ \ 14 \\ 0 & 0 & 10 & 28 & | \ \ 38 \end{matrix} \right] \]