Find the kernel of the linear transformation.
\(\displaystyle T:R^{3} \rightarrow R^{3}, T(x,y,z) = (0,0,0)\)
The answer is \(\displaystyle R^{3}\) However, more reasoning might be needed to show how to get there.
\(\displaystyle 0. 0. 0\) in a vertical line \(\displaystyle = 0. 0. 0\) in a vertical line, so that makes it to be \(\displaystyle R^{3},\). but it wouldn't just be \(\displaystyle (0,0,0)\) as the answer.
\(\displaystyle T:R^{3} \rightarrow R^{3}, T(x,y,z) = (0,0,0)\)
The answer is \(\displaystyle R^{3}\) However, more reasoning might be needed to show how to get there.
\(\displaystyle 0. 0. 0\) in a vertical line \(\displaystyle = 0. 0. 0\) in a vertical line, so that makes it to be \(\displaystyle R^{3},\). but it wouldn't just be \(\displaystyle (0,0,0)\) as the answer.
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