Question

1. An affine transformation $T: \mathbb{R}^n \to \mathbb{R}^m$ has the form $T(x) = Ax + b$, with $A$ an $m \times n$ matrix and $b$ is in $\mathbb{R}^m$. Show that $T$ is linear if and only if $b = 0$. 2. Let $T: \mathbb{R}^n \to \mathbb{R}^m$ be a linear transformation, and let \{$v_1, v_2, v_3$\} be linearly dependent. Is the set \{$T(v_1), T(v_2), T(v_3)$\} linearly dependent? Explain why or why not

          1. An affine transformation $T: \mathbb{R}^n \to \mathbb{R}^m$ has the form $T(x) = Ax + b$, with $A$ an $m \times n$ matrix and $b$ is in $\mathbb{R}^m$. Show that $T$ is linear if and only if $b = 0$.
2. Let $T: \mathbb{R}^n \to \mathbb{R}^m$ be a linear transformation, and let \{$v_1, v_2, v_3$\} be linearly dependent. Is the set \{$T(v_1), T(v_2), T(v_3)$\} linearly dependent? Explain why or why not

$1. An affine transformation T: ℝ^n →ℝ^m has the form T(x) = Ax + b, with A an m × n matrix and b is in ℝ^m. Show that T is linear if and only if b = 0. 2. Let T: ℝ^n →ℝ^m be a linear transformation, and let {v1, v2, v3} be linearly dependent. Is the set {T(v1), T(v2), T(v3)} linearly dependent? Explain why or why not$

Added by Mohamed C.

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