Matrices

Matrices

Equal matrices. Operations on matrices

Poll

How do we call horizontal lines in matrices?

• Row

• Column

Poll

How do we call vertical lines in matrices?

• row

• column

Poll

What is the dimension of the given  matrix?

• 5x4

• 4x5

Poll

What are  $d_{13},\ d_{42},\ d_{24}$  for the given matrix?

• 4,-3, -1

• -4, -1, -3

Poll

How do we call a matrix with same number of rows and columns

• Row matrix

• column matrix

• Rectangular matrix

• Square matrix

Poll

How do we call a matrix with different number of rows and columns?

• Square matrix

• rectangular matrix

• identity matrix

• Diagonal matrix

Poll

How do we call a square matrix whose main diagonal elements are 1 and whose other elements are all zero.

• Identity matrix

• lower triangular matrix

• upper triangular matrix

• Scalar matrix

Poll

How do we call a square matrix in which all the entries below the main diagonal are zero

• Lower triangular matrix

• upper triangular matrix

• scalar matrix

• diagonal matrix

Objectives of the lesson:

• understand the equality of matrices

• perform operation on matrices such as addition, subtraction. Multiplying by a scalar

Equal Matrices

• Two matrices (A and B) are equal if they have the same dimension and their corresponding entries are equal.

Example1:

Find x,y,z from the given matrix

Find a+b+c=?

Multiple Choice

Find x,y,z

• x=7, y=5, z=3

• x=5, y=1, z=5

• x=7, y=4, z=5

• x=-1, y=3, z=5

Addition and subtraction on matrices

Multiple Choice

find x-y=?

• -2

• 5

• 2

• -5

Operations on matrices

• Addition and subtraction

• Multiplying by a scalar

Addition and subtraction of matrices

• Two matrices can be added or subtracted only if they have same order (dimension)

• To add or subtract matrices, just add or subtract the corresponding elements

Properties of addition

Example:

Multiple Choice

• 2

• -2

• 10

• 0

Multiplying by scalar

To multiply matrices by a scalar, just multiply each entry by the scalar

Example:

Multiple Choice

• 2

• -2

• 10

• 0