4.11

Topic

The Inverse and Determinant of a Matrix

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

Sub-standards

• 4.11.A.1 — Determine the inverse of a 2 2 × matrix. The identity matrix, I, is a square matrix consisting of 1s on the diagonal from the top left to bottom right and 0s everywhere else.
• 4.11.A.2 — Multiplying a square matrix by its corresponding identity matrix results in the original square matrix.
• 4.11.A.3 — The product of a square matrix and its inverse, when it exists, is the identity matrix of the same size.
• 4.11.A.4 — The inverse of a 2 2 × matrix, when it exists, can be calculated with or without technology.
• 4.11.B — Apply the value of the determinant t vertibility o in and vectors.
• 4.11.B.1 — a A = c b d The determinant of the matrix is ad b − c. The determinant can be calculated with or without technology and is denoted det(A).
• 4.11.B.2 — If a 2 2 × matrix consists of two column or row vectors from R 2 , then the nonzero absolute value of the determinant of the matrix is the area of the parallelogram spanned by the vectors represented in the columns or rows of the matrix. If the determinant equals 0, then the vectors are parallel.
• 4.11.B.3 — The square matrix A has an inverse if and only if det(A) 0. UNIT 4 Additional Topic Available to Schools