- #1
amcavoy
- 665
- 0
I found this problem on the MIT OpenCourseWare website, but a solution was not given. I tried it out, so I was wondering if my answer is correct. The problem is as follows:
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Suppose A is reduced by the usual row operations to
[tex]R=\begin{bmatrix}1 & 4 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0\end{bmatrix}.[/tex]
Find the complete solution (if a solution exists) to this system involving the original A:
Ax = sum of the columns of A.
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I figured if you took the columns of A and added them together, it would be the same as multiplying a by <1,1,1>. Thus I have the following:
[tex]A\mathbf{x}=A\begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}.[/tex]
So the solution is the vector <1,1,1>. Is this correct?
Thank you.
----------------------------------------------------------
Suppose A is reduced by the usual row operations to
[tex]R=\begin{bmatrix}1 & 4 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0\end{bmatrix}.[/tex]
Find the complete solution (if a solution exists) to this system involving the original A:
Ax = sum of the columns of A.
----------------------------------------------------------
I figured if you took the columns of A and added them together, it would be the same as multiplying a by <1,1,1>. Thus I have the following:
[tex]A\mathbf{x}=A\begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}.[/tex]
So the solution is the vector <1,1,1>. Is this correct?
Thank you.