4.1 MATRIX OPERATIONS

WHAT IS A MATRIX?A group of numbers arranged in rows

and columns.Its numbers are called entries or

elements.The dimensions are:

# of rows x # of columns

Example: This matrix has dimension 2 x 3

SPECIAL MATRICESName Description Example

Row Matrix only 1 row

Column Matrix only 1 column

Square matrix same # of rows and columns

Zero Matrix all entries are zeros

COMPARING MATRICESTwo matrices are equal if their dimensions

are the same and corresponding entries are equal.

Are these equal?

ADDING AND SUBTRACTING MATRICES

Dimensions must match!Add or subtract corresponding entries.

Examples:

Not Possible!

YOUR TURN!Perform the indicated operation, if possible.a.

b.

c.

MULTIPLYING BY A SCALARScalar – a regular numberScalar multiplication – multiplying a

matrix by a scalarJust multiply each entry by the scalar!

Example:

EXAMPLE:

Perform the indicated operation(s), if possible.

YOUR TURN!

Perform the indicated operation(s).

SOLVING MATRIX EQUATIONSSimplify, then write equations for

corresponding entries and solve.Example:Solve for x and y.

YOUR TURN!Solve the matrix equation for x and y: