## Monday, 21 November 2011

### How to find the matrix A if we known of Leontief matrix

How to find the matrix A if we known of Leontif matrix. This post is a continuation of my previous post about the Leontief inverse matrix, as well as to answer questions friend about the inverse matrix, which asks you about how to calculate the matrix technology if we known the Leontief inverse matrix.

If we let the technology matrix is a matrix A, and L is the Leontief inverse matrix.

L = (I - A) -1

then if L will be inverse again , Then will generate a matrix (I - A), illustrated by below equation
L-1 = (I - A) -1 = ((I - A) -1) -1 = (I - A)
then the matrix A can be calculated:
I - A = (I - A)
-A = (I - A)-I
A = absolute((I - A)-I)

Based on equation of the matrix above, then by using excel the above equation can be calculated with the following guidelines:

1. Create a table as below

### How to calculate Leontief matrix in excel

Calculate the Leontief matrix in excel. Leontief matrix is a matrix that is the inverse of identity matrix minus matrix A. Leontief matrix is widely used in making the simulation or quantitative input-output analysis. In mathematical equations used to define the matrix Leontif are:

L = (I - A) -1

where:
L = matrix inverse Leontief
I = Identity Matrix
A = matrix A

By using Microsoft Excel, if we known a matrix A, then the Leontief inverse matrix can be calculated
to be more easily able to see the guidelines below:

1. Create a table matrix A and the identity matrix as below

### How to calculate logarithm addition and logarithm multiplication in excel

How to calculate logarithm addition and logarithm multiplication in excel. By using Microsoft Excel, in addition  to calculate logarithm reduction and log division. Can also be done multiplication and addition of logarithms. In this post the process of logarithm addition and logarithm multiplication refers to the properties of logarithms as below:

ª log a = 1
ª log 1 = 0
ª ⁿ = n log a
ª ⁿ log b = log b n • ª
log ª ª b • c = log b + log c ª
ª log b / c = ª log b - log c ª
ª ⁿ m = m log b / log b n • ª
ª a ÷ b = log b log a
ª b log log b • c • d = c log log d ª
ª b = c log log log a b c ÷

Before applying the formula logarithms , we need using syntax of logarithm in excel as :
LOG (number, base)

With:
Number is the positive real number for which you want the logarithm.
Base is the base of the logarithm. If base is omitted, it is assumed to be 10

One of the properties of logarithms to be used is
log ª ª b • c = log b + log c ª
In order to more easily implement it, can follow the following procedure:
1. Create the table below
Columns A, B, C will contain the data, with a logarithmic base and  number
Colum D and colum W will filled with logarithm formula

### How to calculate logarithm reduction and log division in excel

How to calculate logarithm reduction and log division in excel. By using Microsoft Excel, we can perform the calculation of logarithms. In this post specifically discussed about how to use a logarithmic reduction formula and the division of the logarithm.

In general, how to write formulas / functions in excel logarithms is using syntax:

LOG (number, base)

with:
Number is the positive real number for which you want the logarithm.
Base is the base of the logarithm. If base is omitted, it is assumed to be 10
.

A simple example application of the reduction formula and the distribution of the logarithm can be seen below
ª log b / c = ª log b - log c ª

To calculate in Excel can follow the following procedure:

1. Create a table as below
Column A is the logarithmic base
Columns B and C is filled with data
Column D and E will filled with logaritm formula