2.3 Modeling Real 2.3 Modeling Real World Data with World Data with MatricesMatrices

Matrix – a rectangular array or terms called Matrix – a rectangular array or terms called elements. elements.

Elements are arranged in rows and columns Elements are arranged in rows and columns and enclosed by brackets.and enclosed by brackets.

A matrix with m rows and n columns is an m x A matrix with m rows and n columns is an m x n matrix.n matrix.

The dimensions of the matrix and m and n.The dimensions of the matrix and m and n. Named using a capital letter. Named using a capital letter.

Two matrices are equal if and only if Two matrices are equal if and only if they have the same dimensions and are they have the same dimensions and are identical, element by element.identical, element by element.

Ex 2Ex 24

3 2 1

y x

y x

Addition – can add if Addition – can add if same sizesame size

Ex 3Ex 3

-7 4 6 10

Find A + B if A= 5 0 and B= 8 -9

3 -1 -2 5

Additive Identity – for every Additive Identity – for every matrix A, another matrix matrix A, another matrix can be found so that their can be found so that their sum is A.sum is A.

0 0 - zero matrix

0 0

Ex 4Ex 4

Fins S – T.Fins S – T.

2 -1 3 -5 -4 1 and T=

-4 -2 -8 7 -8 4S

Scalar multiplication –Scalar multiplication – multiply each multiply each element of the matrix by the scalar.element of the matrix by the scalar.

Ex 5Find 4A if A=Ex 5Find 4A if A=

5 -2

3 8

-1 -9

Matrix multiplication – the product of an Matrix multiplication – the product of an m x n matrix and an n x r matrix is an m m x n matrix and an n x r matrix is an m x r matrix.x r matrix.

Ex 6 Ex 6

Find ABFind AB

Find BCFind BC

4 -1 2 4 2 1 2 -3

0 1 0 B= C= -2 3 3 1 0

3 -2 4

A

Ex 7Ex 74 -2 3

-6 -1 05 0 -1

1 4 0 9 0 1