DATE: ______________
Unit 8 (Chapter 6 & 7): Matrices & Vectors Pre-Calculus 2018-2019
7.3 Solve Systems of Equations Using Matrices
Target 8F: 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 × 3 or greater).
Review of Prior Concepts
Find the equation of a parabola that passes through the points (−1,9), (1,5), and (2,12) using Inverse
Matrices.
More Practice
Solving Systems Using Inverse Matrices
http://www.mathplanet.com/education/algebra-2/matrices/using-matrices-when-solving-system-of-
equations
http://math.uww.edu/~mcfarlat/matrix.htm
https://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html
https://youtu.be/Re1F4d24Fxc
https://youtu.be/0_DYEFtlCiM
https://youtu.be/FlLsxlWD6a8
Augmented Matrices
Augmented Matrix – one matrix with coefficients and answers
Example:
Write the system of equations as an augmented matrix: {𝑥−2𝑦+𝑧=7
3𝑥−5𝑦+𝑧=14
2𝑥−2𝑦−𝑧=3
Solving Augmented Matrices
To solve an augmented matrix,
use Gaussian elimination to have the matrix in Reduced Row Echelon Form.
Reduced Row Echelon Form:
[
1 0 0
0 1 0
0 0 1 ⋯ 0 𝑎1
⋯ 0 𝑎2
⋮ ⋮ ⋮
0 0 0 ⋱ ⋮ ⋮
⋯ 1 𝑎𝑛
]
