- #1
JoshMaths
- 26
- 0
Homework Statement
$$
\begin{pmatrix}
-1&3&0\\
2&0&-1\\
0&-6&1
\end{pmatrix}
$$
Finding the ImT basis of this
The Attempt at a Solution
I got it down to
$$
\begin{pmatrix}
1&0&-1/2\\
0&1&1/6\\
0&0&1
\end{pmatrix}
$$
I know that by the principle of having pivots as the only non-zero entities in their respective columns this makes that column one of the basis vectors. So answer is
[-1,2,0] [3,0,-6]
What i don't understand is why (In the r-echelon form) i cannot subtract -1/2(Row 3) from Row 1 and Subtract 1/6(Row 3) from Row 2 to give the Guass-Jordan form or Identity form which would imply that the entire first matrix was a basis for itself right? Meaning the basis contains three vectors instead of the actual two is contains in the correct answer.
Thanks, and i hope the question has come out clearly, just say if clarification is needed.
Josh
Last edited: