PPT - Matrices and Determinants B Com Notes | EduRev

Business Mathematics and Statistics

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B Com : PPT - Matrices and Determinants B Com Notes | EduRev

 Page 1


MATRICES AND 
DETERMINANTS
Page 2


MATRICES AND 
DETERMINANTS
OBJECTIVES
Definition and examples of Matrices
Types of Matrices
Addition and Subtraction of Matrices
Multiplication and Division of Matrices
Definition and examples of Determinants
Cramer’s method for 2 ?2 and 3 ?3 systems (variables).
Relationship between Matrices and Determinants, with examples
Solution of the case using Cramer’s method
Page 3


MATRICES AND 
DETERMINANTS
OBJECTIVES
Definition and examples of Matrices
Types of Matrices
Addition and Subtraction of Matrices
Multiplication and Division of Matrices
Definition and examples of Determinants
Cramer’s method for 2 ?2 and 3 ?3 systems (variables).
Relationship between Matrices and Determinants, with examples
Solution of the case using Cramer’s method
Matrices
A matrix is a rectangular arrangement of numbers into rows and columns.
The number of rows and columns that a matrix has is called its dimension or its 
order. By convention, rows are listed first; and columns, second.
Numbers that appear in the rows and columns of a matrix are called elements of 
the matrix.Two matrices are equal if all three of the following conditions are met:
? Each matrix has the same number of rows.
? Each matrix has the same number of columns.
? Corresponding elements within each matrix are equal.
Page 4


MATRICES AND 
DETERMINANTS
OBJECTIVES
Definition and examples of Matrices
Types of Matrices
Addition and Subtraction of Matrices
Multiplication and Division of Matrices
Definition and examples of Determinants
Cramer’s method for 2 ?2 and 3 ?3 systems (variables).
Relationship between Matrices and Determinants, with examples
Solution of the case using Cramer’s method
Matrices
A matrix is a rectangular arrangement of numbers into rows and columns.
The number of rows and columns that a matrix has is called its dimension or its 
order. By convention, rows are listed first; and columns, second.
Numbers that appear in the rows and columns of a matrix are called elements of 
the matrix.Two matrices are equal if all three of the following conditions are met:
? Each matrix has the same number of rows.
? Each matrix has the same number of columns.
? Corresponding elements within each matrix are equal.
Examples Of Matrices
Its dimensions are 2 ×3
2 rows and three columns
The entries of the matrix below are 2, -5, 
10, -4, 19, 4.
The variable A in  the matrix equation below represents 
an entire matrix.
Page 5


MATRICES AND 
DETERMINANTS
OBJECTIVES
Definition and examples of Matrices
Types of Matrices
Addition and Subtraction of Matrices
Multiplication and Division of Matrices
Definition and examples of Determinants
Cramer’s method for 2 ?2 and 3 ?3 systems (variables).
Relationship between Matrices and Determinants, with examples
Solution of the case using Cramer’s method
Matrices
A matrix is a rectangular arrangement of numbers into rows and columns.
The number of rows and columns that a matrix has is called its dimension or its 
order. By convention, rows are listed first; and columns, second.
Numbers that appear in the rows and columns of a matrix are called elements of 
the matrix.Two matrices are equal if all three of the following conditions are met:
? Each matrix has the same number of rows.
? Each matrix has the same number of columns.
? Corresponding elements within each matrix are equal.
Examples Of Matrices
Its dimensions are 2 ×3
2 rows and three columns
The entries of the matrix below are 2, -5, 
10, -4, 19, 4.
The variable A in  the matrix equation below represents 
an entire matrix.
Types Of Matrices
Vectors
Vectors are a type of matrix having only one column or one row.
? Row vector or row matrix
? Column matrix or column vector
? Square Matrix
A matrix in which numbers of rows are equal to number of columns is called a 
square matrix
Diagonal Matrix
A square matrix A is called a diagonal matrix if each of its non-diagonal element is 
zero. 
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