Thread: matrix equation.

hello can someone please demonstrate how matrix is evaluated by expressing it in echelon form and use row reduction to solve it. it would be a great help.

k1+ L2+ Z = 20
3K -L+2Z = 22
2K+L-4Z=7

Originally Posted by sigma1

hello can someone please demonstrate how matrix is evaluated by expressing it in echelon form and use row reduction to solve it. it would be a great help.

k1+ L2+ Z = 20
3K -L+2Z = 22
2K+L-4Z=7

Actually, it is the other way around- row reduce in order to get the echelon form.

The "augmented matrix" for this system is $\displaystyle \begin{bmatrix} 1 & 2 & 1 & 20 \\ 3 & -1 & 2 & 22 \\ 2 & 1 & -4 & 7\end{bmatrix}$.

Now use row operations to put this into echelon form. For example, a first step would be to subtract three times the first row from the second row and subtract two times the first row from the third row:
$\displaystyle \begin{matrix}1 & 2 & 1 & 20 \\ 0 & -7 & -1 & -38 \\ 0 & -3 & -6 & -33\end{bmatrix}$
That take care of the first row. Now subtract 3/7 times the second row from the third row.

Originally Posted by HallsofIvy

Actually, it is the other way around- row reduce in order to get the echelon form.

The "augmented matrix" for this system is $\displaystyle \begin{bmatrix} 1 & 2 & 1 & 20 \\ 3 & -1 & 2 & 22 \\ 2 & 1 & -4 & 7\end{bmatrix}$.

Now use row operations to put this into echelon form. For example, a first step would be to subtract three times the first row from the second row and subtract two times the first row from the third row:
$\displaystyle \begin{matrix}1 & 2 & 1 & 20 \\ 0 & -7 & -1 & -38 \\ 0 & -3 & -6 & -33\end{bmatrix}$
That take care of the first row. Now subtract 3/7 times the second row from the third row.

I have tried that but am not arriving at a correct answer. could you please show me what you would get for the matrix in triangular form.

Originally Posted by sigma1

I have tried that but am not arriving at a correct answer. could you please show me what you would get for the matrix in triangular form.

You might want to use this to find out where you are going wrong:

Linear Algebra Toolkit

Originally Posted by harish21

You might want to use this to find out where you are going wrong:

Linear Algebra Toolkit

thanks a million...