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Math  /  Algebra

QuestionExample 5.2.1. Let T(x1,x2,x3)=(x1−x2,−2x1+2x2+x3,−x1+x2+x3)T\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}-x_{2},-2 x_{1}+2 x_{2}+x_{3},-x_{1}+x_{2}+x_{3}\right) and b⃗=(1,0,−1)\vec{b}=(1,0,-1). Determine whether b⃗∈T(R3)\vec{b} \in T\left(\mathbb{R}^{3}\right).

Studdy Solution
Since there's no solution to the system, the vector (1,0,−1)(1, 0, -1) is *not* in the range of the transformation TT.
So, b⃗∉T(R3)\vec{b} \notin T(\mathbb{R}^3).

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