Definition of matrixes

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Matrixes

By : Sonia Nurdiansa, S.Si

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Today’s Lesson

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Definition of Matrices

Today’s Lesson

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Definition of Matrices Types of Matrices

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Adding & Subtracting Matrices

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Adding & Subtracting Matrices

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Multiplying Matrices

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Definition

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Definition

A matrix is a rectangular arrangement of numbers or

constants into rows and columns.

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Definition

A matrix is a rectangular arrangement of numbers or constants into rows and columns.

A = [ ] a b c d e f

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Definition

A matrix is a rectangular arrangement of numbers or constants into rows and columns.

rows columns

A = [ ] a b c d e f

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0 Vocabularies

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Number of rows by number of columns of a matrix.

Vocabularies

Dimension

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Vocabularies

Dimension

A = [ ] a b c d e f

dimensions 2X3 or called A

2X3

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Vocabularies

Dimension

A = [ ] a b c d e f

2X3

Element

Each Value in a matrix, either a

number or a constant.

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Vocabularies

Dimension

A = [ ] a b c d e f

2X3

Element

Each Value in a matrix, either a number or a constant.

A = [ ] a b c d e f

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Vocabularies

Dimension

A = [ ] a b c d e f

2X3

Element

Each Value in a matrix, either a number or a constant.

A = [ ] a b c d e f

A = a, A = b, A = c A = d, A = e, A = f

1,1 1,2 1,3

2,1 2,2 2,3

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Types of Matrices

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Types of Matrices

Column Matrix

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Types of Matrices Column Matrix

A matrix with only one

column.

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Types of Matrices Column Matrix

A matrix with only one column.

A = [ ] d a

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Types of Matrices Column Matrix Row Matrix

A matrix with only one column.

A = [ ] d a

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column. A matrix with only one row.

A = [ ] d a

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column. A matrix with only one row.

A = [ ] d a A = [ ] a b c

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Types of Matrices

Column Matrix Row Matrix Square Matrix

column. A matrix with only one row.

A = [ ] d a A = [ ] a b c

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Types of Matrices

column. A matrix with only one row. A matrix that has the same number of rows and

columns.

A = [ ] d a A = [ ] a b c

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Types of Matrices

column. A matrix with only one row. A matrix that has the same number of rows and

columns.

A = [ ] d a A = [ ] a b c A =

[ ] d e a b

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Adding and Subtracting Matrices

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To add and subtract two matrices, they must have

the same dimensions.

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To add and subtract two matrices, they must have the same dimensions.

[ ] a b c d e f + = [ ] g h i j k l

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Adding and Subtracting Matrices

To add and subtract two matrices, they must have the same dimensions.

[ ] a b c d e f + = [ ] g h i j k l [ ] a+g b+h c+i

d+j e+k f+l

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Examples

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0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

Examples

Adding

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1 1

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3 3

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5 5

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0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

Examples

Adding

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8 8

1 1

4 4

9 9

6 6

3 3

7 7

5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

Examples

Adding

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8 8

1 1

4 4

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3 3

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5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

Examples

Adding

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8 8

1 1

4 4

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3 3

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5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

Examples

Adding

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8 8

1 1

4 4

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3 3

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5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

Examples

Adding

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8 8

1 1

4 4

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3 3

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5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

[ ]

^{8 5 6}^{3 7 7}

- = [ ]

^{1 3 3}^{2 1 4}

Examples

Adding Subtracting

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1 1

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3 3

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5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

[ ]

^{8 5 6}^{3 7 7}

- = [ ]

^{1 3 3}^{2 1 4}

[ ]

1 6 3 7 2 3

Examples

Adding Subtracting

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8 8

1 1

4 4

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3 3

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5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

[ ]

^{8 5 6}^{3 7 7}

- = [ ]

^{1 3 3}^{2 1 4}

[ ]

1 6 3 7 2 3

[ ]

^{6 4}^{8 5}^{9 5}

- = [ ]

^{2 3}^{5 3}^{1 2}

Examples

Adding Subtracting

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8 8

1 1

4 4

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3 3

7 7

5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

[ ]

^{8 5 6}^{3 7 7}

- = [ ]

^{1 3 3}^{2 1 4}

[ ]

1 6 3 7 2 3

[ ]

^{6 4}^{8 5}^{9 5}

- = [ ]

^{2 3}^{5 3}^{1 2}

[ ]

^{4 1}^{3 2}^{8 3}

Examples

Adding Subtracting

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8 8

1 1

4 4

9 9

6 6

3 3

7 7

5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

[ ]

^{8 5 6}^{3 7 7}

- = [ ]

^{1 3 3}^{2 1 4}

[ ]

1 6 3 7 2 3

[ ]

^{6 4}^{8 5}^{9 5}

- = [ ]

^{2 3}^{5 3}^{1 2}

[ ]

^{4 1}^{3 2}^{8 3}

- =

[ ]

^{2 7}^{1 5}

Examples

Adding Subtracting

[ ]

^{1 4}^{1 7}

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8 8

1 1

4 4

9 9

6 6

3 3

7 7

5 5

2

0 2

0 [ ]

^{2 7 4}

1 5 3

+ = [ ]

^{8 3 6}^{2 1 7}

[ ]

4 8 11 9 8 9

[ ]

^{2 3}^{5 3}^{1 2}

+ = [ ]

^{6 1}^{4 3}^{6 5}

[ ]

^{8 4}^{9 6}^{7 7}

[ ]

^{2 3}^{5 3}^{1 2}

+ =

[ ]

^{2 7 4}^{1 5 3}

[ ]

^{8 5 6}^{3 7 7}

- = [ ]

^{1 3 3}^{2 1 4}

[ ]

1 6 3 7 2 3

[ ]

^{6 4}^{8 5}^{9 5}

- = [ ]

^{2 3}^{5 3}^{1 2}

[ ]

^{4 1}^{3 2}^{8 3}

- =

[ ]

^{2 7}^{1 5}

Examples

Adding Subtracting

[ ]

^{1 4}^{1 7}

[ ]

^{1 0}^{0 1}

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Multiplying Matrices

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Multiplying Matrices

There are 2 kinds of multiplying matrices : Multiply a matrix by a scalar

Multiply a matrix by another matrix

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Multiplied by a scalar

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To multiply a matrix by a single number (n), every single element

must be multiplied by that number (n).

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must be multiplied by that number (n).

[ ] nxa nxb nxc nxd nxe nxf

nxA =

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Multiplied by a scalar Examples

[ ] nxa nxb nxc nxd nxe nxf

nxA =

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A is a matrix that has 3 rows and 2

columns. The elements of A are 1 2, 3 4, 5 6. There is a scalar n = 2.

Calculate A multiplied by n !

nxA =

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A is a matrix that has 3 rows and 2

columns. The elements of A are 1 2, 3 4, 5 6. There is a scalar n = 2.

nxA = [ ]

2x1 2x2

2x3 2x4 2x5 2x6

n x A =

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A is a matrix that has 3 rows and 2

columns. The elements of A are 1 2, 3 4, 5 6. There is a scalar n = 2.

nxA =

[ ]

^{10 12}^{2 4}^{6 8}

=

[ ]

2x1 2x2 2x3 2x4

2x5 2x6

n x A =

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You did great.

Thank You!!!