What are the steps or any guidance in solving this problem? I'm very confused
2026-03-29 13:40:32.1774791632
Linear transformation with range of a vector
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The matrix $A$ is a 3x5 matrix. We are given that $T(v) = Av $ where $T: \mathbb{R}^5 \to \mathbb{R}^3$. The given vector $(3,2,1)^T$ being in $\mathbb{R}^3$ means that it is in the range of $T$. To find all vectors that are mapped to that vector, let $v= (v_1,v_2,v_3,v_4,v_5) $ and solve
$$ Av = (3,2,1)^T $$