Matrix Method Posting

Varong PongsaiFaculty of Accountancy, Rangsit

University, Thailand

Is it possible to adapt any other Mathematics technique to accounting procedure?

Which one is the most suitable for apply to accounting procedure?

If it is possible, how does that work?

Introduction: Motivation

To provide a new perspective of thinking and doing Accounting.

To prove the possibility of applying Mathematics application.

Introduction: Objectives of the study

Accounting Matrix can be used in an accounting procedure.

Accounting is easy access with other perspectives (Formal science perspective).

Introduction : Benefits of this study

Deductive Approach

I. Logical Comparison

II. Logical Investigation

III. Theory Comparison

IV. Empirical Application Testing

Research Methodology

There are 4 concepts for generating or discovering laws and theories

Dreams

Eureka

Deductive Approach

Inductive Approach

Context of discovery

Discovery: Matrix Application for Accounting procedure

Logic: Cause and Result Cause Mathematics is in an accounting procedure.

Result

Matrix can be placed in accounting procedure.

The Major Discovery and Logic

I. Logical Comparison

Accounting Logic Matrix Logic

2 sides operation in one time

Debit - Credit Operation

Balancing amount between 2 sides of operations

2 sides operation in one time

Roll - Column Operation

Balancing amount between 2 sides of operations

Accounting LogicDr. Equipment 100 and Dr. Utility expense

20Cr. Account Payable 100 Cr. Cash 20

Matrix Logic (Roll = Debit and Column = Credit)

I. Logical Comparison

Assets Liabilities Equity Revenue Expense Total

Assets 100 100

Liabilities

Equity

Revenue

Expense 20 20

Total 20 100 120

Asset’s debit = 100

Expense’s debit = 20

Liabilities’ credit = 100Asset’s credit = 20

Rough Trial Balance = 120

Assets Liabilities Equity Revenue Expense Total

Assets

Liabilities

Equity

Revenue

Expense

Total

Matrix Explanation

Debit Operation

Credit OperationPutting the number in 1 cell,

It will effect 2 sides.

Assets + Expense = Liabilities + Equity + Revenue (Debit side) (Credit Side)

II. Logical InvestigationAccounting Logic Matrix Logic

Dynamic movementAsset + Expense = Liability + Owner’s equity +

Revenue

(Debit) (Credit)

Expense - Liability = Owner’s equity + Revenue - Asset

(Debit) (Credit)

Dynamic Logic

DeterminantCross Product Method >> Small dimension matrix

Minor Method >> Large dimension matrix

Roll Minor = Column Minor

TransposeSwitch Roll and Column Operation

Inverse Calculation

Operating Business

)(

)(1

ADet

AAdjA

Components changing

Basic assumption for business activity

Liabilities increasing Purchasing assets on creditEquity increasing Initial investment by assetsRevenues increasing Selling merchandise for cashExpenses decreasing Adjusting prepaid expense by full expense

method

III.Theory ComparisonFormal Science Paradigm Social Science Paradigm

Exist in the nature

Use to identify natural logic

Mathematics is an essential tool.

Every natural appearance can be explained by mathematics’ function

Generated by human needs

Use to search for relationship

Statistics is a key for measurement.

Every relationship is provided and proved by statistics’ model.

Which one is closely to accounting?

Accounting has something strange for classifying.

Accounting uses basic mathematics’ operation.

Accounting depends on equation.

Accounting does not use to identify any appearance.

Accounting does not use statistics’ model.

Accounting does not exist in the nature.

III.Theory Comparison

Accounting is an example of hybrid paradigm

Mathematics’ operation – Formal science

Depends on equation – Formal science

Do not identify appearance – Social science

Do not exist in the nature – Social science

III.Theory Comparison

Light Appearance Study

- Light sometimes is a particle.

- Light sometimes is a wave.

Physics (Formal Science) calls Light as

“Dual Nature of Appearance”

III.Theory Comparison

Brought to Accounting by formal science

Accounting sometimes is Formal science.

Accounting sometimes is Social science.

Accounting should be called as

“Dual Nature of Appearance.”

III.Theory Comparison

For example;

“Purchase equipment 100 Baht on account”

What should accounting do with this transaction?

IV. Empirical Application Testing

1.Selecting Set of Element

2.Determining accounting logic

IV. Empirical Application Testing

Business Meaning Set of Element

Obtaining equipment Asset

Generating debt Liability

Business Meaning Logical thinking Side of Equation

Obtaining equipment

Asset is increasing Debit

Generating debt Liability is occurring Credit

3. Matrix and Real number Operation – Operating

(Assuming: Roll – Debit , and Column – Credit)

IV. Empirical Application Testing

Asset Liability Equity Revenue Expense Total

Asset 100 100

Liability

Equity

Revenue

Expense

Total 100 100

Total Debit = 100

Total Credit = 100

Total Debit = Total Credit

For example;

“Receive Utility Bill 20 Baht, paid cash only 15 Baht”

A classic way is as follow:

What’s about the new one?

IV. Empirical Application Testing

Transaction Reff. No.

Debit Credit

Utility expense 20

Cash Utility payable

155

1. Selecting Set of Element

2. Determining accounting logic

IV. Empirical Application Testing

Business Meaning Set of Element

Consuming utility from provider Expense

Paying cash to utility provider Asset

Delaying payment to provider Liability

Business Meaning Logical Thinking Side of equation

Consuming utility from provider

Expense is occurring Debit

Paying cash to utility provider Asset is decreasing Credit

Delaying payment to provider Liability is occurring Credit

3. Matrix and Real Number Operation – Operating

IV. Empirical Application Testing

Asset Liability Equity Revenue Expense Total

Asset 100 100

Liability

Equity

Revenue

Expense 15 5 20

Total 15 105 120

Asset Cr. = 15

Liability Cr. = 105

Asset Dr. = 100

Expense Dr. = 20

Total Dr. = Total Cr.

Logic : Cause; The fundamental operation can work.Result; The signature operation should work.

Signature Operation : Determinant Calculation

“Because, Accounting Matrix is a singular matrix.

Determinant must be equal 0” (det(A) = 0)

Additional Empirical Testing

Problem :

Is it truly that the determinant must be equaled to “0”?

Answer: It must be “0” because there are impossible transactions lying in the accounting dynamics.

For example;

These make the Matrix containing a lot of “0” in the cells.

Additional Empirical Testing

Impossible of revenue Impossible of expense

Dr. Equity XXX Cr. Revenue XXX

Dr. Expense XXX Cr. Equity XXX

How does determinant use in accounting?

Determinant calculation is useful to check how accuracy of accounting procedure is.

Who is the most appropriate user?

Auditor should be the most appropriate user, because this job concerns about the accuracy of accounting procedure.

Additional Empirical Testing

Accounting Matrix is proved for existing by the Deductive Approach.

Accounting Matrix can place for a classic way of recording possibly.

Formal science can be integrated into Social science procedure smoothly.

Formal science will cross over to Social science when the procedure is obviously providing

“Dual nature of appearance”.

Summary and Conclusion

The Accounting Matrix should also explain the surplus from combining between business

entities.(A and B are used for an entity matrix)

Merger: A + B = cA “c” stands for scalar of surplus proportion after merger procedure.

Consolidation: A + B = C“C” is a new matrix entity after consolidation.

Future research

Thank you