Vault Of Euclid

Evaluating a Non-Linear Mapping and Finding a Preimage

Linear transformations warmup

Consider the mapping \( F: \mathbb{R}^3 \to \mathbb{R}^2 \) defined by \( F(x,y,z) = (yz, x^2) \). Find
  • [(a)] \( F(2,3,4) \);
  • [(b)] \( F(5, -2, 7) \);
  • [(c)] \( F^{-1}(0,0) \), that is, all \( v \in \mathbb{R}^3 \) such that \( F(v) = 0 \).
mappingfunction-evaluationpreimagenon-linear-mapcoordinate-geometryzero-locussystem-of-equationsvector-spaceslinear-algebra

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What you need first

What this problem tests

Tests the ability to substitute values into a mapping and solve a simple system of equations to find a preimage.

This is a foundational exercise in understanding mappings between vector spaces, often encountered early in a linear algebra or multivariable calculus course.

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