1. ## Finding Elementary Matrix

I have a problem I need help with. I have the following Matrix A:

$\displaystyle \begin{array}{ccccc} 6 & 4 & -1 & 2 & 5\\ 3 & 0 & -1 & 2 & 7 \\ 18 & 3 & 4 & -2 & 0 \\ 6 & 8 & 0 & 0 & -4 \end{array}$

I need to find an elementary matrix with subtracts 2 times column 4 from column 2 of matrix A.

I have no idea where to start, and I can't find a good reference source.

2. Originally Posted by notgod
I have a problem I need help with. I have the following Matrix A:

$\displaystyle \begin{array}{ccccc} 6 & 4 & -1 & 2 & 5\\ 3 & 0 & -1 & 2 & 7 \\ 18 & 3 & 4 & -2 & 0 \\ 6 & 8 & 0 & 0 & -4 \end{array}$

I need to find an elementary matrix with subtracts 2 times column 4 from column 2 of matrix A.

I have no idea where to start, and I can't find a good reference source.
This is easier than it seems. Elementary matrices are just matrices that result from elementary matrix operations. For this problem, look at columns 4 and 2. Can you find $\displaystyle 2*C_4$? I bet so. What about $\displaystyle C_2-2*C_4$? I bet so.

Now the new matrix will be the starting one with column 2 being changed to the answer from above.

3. Originally Posted by notgod
I have a problem I need help with. I have the following Matrix A:

$\displaystyle \begin{array}{ccccc} 6 & 4 & -1 & 2 & 5\\ 3 & 0 & -1 & 2 & 7 \\ 18 & 3 & 4 & -2 & 0 \\ 6 & 8 & 0 & 0 & -4 \end{array}$

I need to find an elementary matrix with subtracts 2 times column 4 from column 2 of matrix A.

I have no idea where to start, and I can't find a good reference source.
I think you are confusing terminology. An "elementary matrix" doesn't depend on a "matrix A". If you are looking for an elementary matrix that "subtracts 2 times column 4 from column 2" of any matrix it multiplies, just set up the 5 by 5 identity matrix and subtract two times column 4 from column 2 of it. That is, all except column 2 will be unchanged and it will just have a "-2" in the 4th row, in addition to the "1" in the second row.