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  3. ZuAI AP College Board Pre-Calculus
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Question BankQuestion Bank

Linear Transformations and Matrices

Tom Green

Tom Green

8 min read

Next Topic - Matrices as Functions
Study Guide Overview

This study guide covers linear transformations and matrices, focusing on how matrices represent these transformations. Key concepts include the properties of linear transformations (preserving addition and scalar multiplication), the zero vector, representing single and multiple vectors in R² using matrices, transformation matrices, and matrix multiplication. The guide also provides practice questions and exam tips covering common question types, time management, and potential pitfalls.

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Previous Topic - The Inverse and Determinant of a MatrixNext Topic - Matrices as Functions

Question 1 of 4

Which of the following operations is NOT preserved under a linear transformation TTT?

Vector addition: T(u+v)=T(u)+T(v)T(u + v) = T(u) + T(v)T(u+v)=T(u)+T(v)

Scalar multiplication: T(cu)=cT(u)T(cu) = cT(u)T(cu)=cT(u)

Mapping zero vector to zero vector: T(0)=0T(0) = 0T(0)=0

Vector multiplication: T(uv)=T(u)T(v)T(uv) = T(u)T(v)T(uv)=T(u)T(v)