MA19.PRE.23

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.23
Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).

Unpacked Content

Knowledge

Students know:

Procedures for converting systems of equations to matrix equations.
Conditions that determine the inverse of a matrix exists.
Techniques for determining the inverse of a matrix (including using technology).
Process for using the inverse of a matrix to find the solution to a matrix equation (2 x 2).
Matrix multiplication is not commutative.

Skills

Students are able to:

Perform row operations on a matrix to find the inverse of the matrix.
Efficiently and accurately find the inverse of a matrix using technology.

Understanding

Students understand that:

The solutions to a matrix equation are the solutions to the system of equations that produced the matrix equation.
Solving a matrix equation is analogous to solving a linear equation.
Technology is a useful tool that facilitates investigation and, once the initial process is understood, helps find solutions of more complex problems.

Vocabulary

Inverse of a matrix
Dimension of a matrix

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