AP PreCalculus Flashcards: Linear Transformations and Matrices
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What does the equation L(v⃗) = Av⃗ represent?
This equation represents that the action of a linear transformation L on a vector v⃗ is equivalent to the matrix-vector product of the transformation's unique matrix A and the vector v⃗.
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What does the equation L(v⃗) = Av⃗ represent?
This equation represents that the action of a linear transformation L on a vector v⃗ is equivalent to the matrix-vector product of the transformation's unique matrix A and the vector v⃗.
When a 2x2 transformation matrix is multiplied by a 2xn matrix of input vectors, what are the dimensions of the resulting matrix?
The resulting matrix will have dimensions of 2xn, where each column is the output vector corresponding to the respective input vector.
Describe the composition of an output vector's components in a linear transformation.
Each component of the output vector is formed by the sum of constant multiples of the input vector's components.
How do you determine the output vector of a linear transformation using its corresponding 2x2 matrix A?
To find the output vector, you multiply the 2x2 transformation matrix A by the input vector v⃗.
Is the 2x2 matrix associated with a specific linear transformation from R² to R² unique?
Yes, for any given linear transformation L from R² to R², there is a unique 2x2 matrix A that represents it.
How can you apply a single linear transformation to multiple input vectors at once using matrices?
You can multiply the 2x2 transformation matrix by a 2xn matrix containing the n input vectors as its columns.
Define a transformation matrix.
For a linear transformation from R² to R², the transformation matrix is the unique 2x2 matrix A such that the transformation of any vector v⃗ is given by the product Av⃗.
What is the relationship between a linear transformation L from R² to R² and a matrix?
For every linear transformation L from R² to R², there is a unique 2x2 matrix, A, that represents the transformation such that L(v⃗) = Av⃗.
What is a linear transformation?
A linear transformation is a function that maps an input vector to an output vector, where each component of the output vector is the sum of constant multiples of the input vector components.
What does the product of a 2x2 transformation matrix A and a 2xn matrix of n input vectors represent?
The product is a 2xn matrix of the n output vectors that result from applying the linear transformation to each of the n input vectors.