Define $T$ on $R^3$ as $T(x, y, z) = (2y + z, x - 4y, 3x)$ for any $x…

Question

Define $T$ on $R^3$ as

$T(x, y, z) = (2y + z, x - 4y, 3x)$

for any $x, y, z \in R$ where $R$ is the set of all reals. Then show that $T$ is linear and also find the matrix associated with $T$ relative to the basis set $B = \{(1, 1, 1), (1, 1, 0), (1, 0, 0)\}$.

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