Statistics Solutions

[Solution] Let V=(x, y, z) ∈ R^3 \mid x+2 y-3 z=0, and let T: V \rightarrow R^3 be given by T(x, y, z)=(x+y, y-z, z) Show that T is a linear transformation.

Question: Let $V=\left\{(x, y, z) \in \mathbb{R}^{3} \mid x+2 y-3 z=0\right\}$, and let $T: V \rightarrow \mathbb{R}^{3}$ be given by $T(x, y, z)=(x+y, y-z, z)$

Show that $T$ is a linear transformation.
Find the kernel and range of $T$, and the dimension of each.
What does the rank-nullity theorem tell you in this case?

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[Solution] Let V=(x, y, z) ∈ R^3 \mid x+2 y-3 z=0, and let T: V \rightarrow R^3 be given by T(x, y, z)=(x+y, y-z, z) Show that T is a linear transformation.

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