MATRICES
8.1
BIG IDEAS…
1.
We can treat matrices like other types of
numbers and talk about adding, subtracting,
multiplying, “dividing”
2.
We can use matrices as a tool to solve linear
systems
  The
Goal:
To have a some basic background about matrices
AND
  To solve linear systems with matrices.

MATRIX VOCAB.

Matrix (matrices)

Order

Entries of a matrix

Main diagonal

Square Matrix

Column Matrix (column vector)

Row Matrix (row vector)
COEFFICIENT & AUGMENTED MATRICES
  Coefficient
Matrix
  Augmented
Matrix
Linear Systems and Matrices are related.
  Row-echelon



Form
All zero rows at the bottom
Has leading 1 in every nonzero row
All entries below leading 1’s are zero.
  Reduced
row-echelon Form
All zero rows at the bottom
  Has leading 1 in every nonzero row
  All entries below leading 1’s are zero.
AND
  All entries above leading 1’s are also zero.

ELEMENTARY ROW OPERATIONS:
①
Exchange two rows (equations)
②
Multiply a row (equation) by a nonzero constant
③
Add two rows (equations) and replace one of the
rows used with the result.