4.13

Topic

Matrices as Functions

Practice by unit: Functions Involving Parameters, Vectors, and Matrices

Sub-standards

• 4.13.A.1 — Determine the association between a linear transformation and a matrix. The linear transformation mapping to + is associated with a a 11 12 . a a 21 22the matrix
• 4.13.A.2 — The mapping of the unit vectors in a linear transformation provides valuable information for determining the associated matrix.
• 4.13.A.3 — cos −sin sin is associated with a linear transformation of vectors that rotates every vector an angle counterclockwise about the origin. cos The matrix
• 4.13.A.4 — The absolute value of the determinant of a 2 2 × transformation matrix gives the magnitude of the dilation of regions in R 2 under the transformation.
• 4.13.B.1 — Determine the composition of two linear transformations. The composition of two linear transformations is a linear transformation.
• 4.13.B.2 — The matrix associated with the composition of two linear transformations is the product of the matrices associated with each linear transformation. UNIT 4
• 4.13.C.1 — Determine the inverse of a linear transformation. Two linear transformations are inverses if their composition maps any vector to itself.
• 4.13.C.2 — If a linear transformation, L, is given by → → L v( ) = Av , then its inverse transformation is given by − A 1 L v −1 → −1→ ( ) = A v, where is the inverse of the matrix A. UNIT 4