# Matrix and it's application

31. Oct 2016
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### Matrix and it's application

• 2. MOHAMMAD AKASH ID:029 FATEMA TABASSUM ID:027 JOYONTO MALLIK ID:002 SHUVRO BANIK ID:011 ESHITA YESMIN ID:035 KARTIK SARMA ID:043
• 3. It is an collection of element which is arranges in rows and columns MATRIX It is the combination of linear equation It is represented by these symbols : () , [] , l l
• 4. TYPES OF MATRIX 1. Row matrices – A matrices which has only one row called row matrices e.g.- [123]1*3 2. Column matrices – A matrices which has only one column is called column matrices e.g. – 1 2 3 3 ∗ 1
• 5. TYPES OF MATRIX 3. Square matrices – No. of the rows and No. of the column is same e.g. 123 456 789 3 ∗ 3 4. Null matrices – Which all elements is equal to ‘0’ 000 000 000 3 ∗ 3
• 6. TYPES OF MATRIX 5. Identity matrices – A square matrices who’s main diagonal is assinty value ‘1’ and each of the other element is ‘0’ e.g 100 010 001 3 ∗ 3 , 10 01 2 ∗ 2, 1 1 ∗ 1 5. Diagonal matrices – A square matrices all of who’s element expect those in the leading diagonal are ‘0’ e.g. - 100 050 009 3 ∗ 3
• 7. TYPES OF MATRIX 7. Scalar matrices – A diagonal matrices in which all the elements of main diagonal is same called scalar matrices e.g.- 200 020 002 3*3 8.Transpose Matrices – A matrices obtained by inter changing the rows and columns of a matrices A It is denoted by A’ , AT e.g.:- A⇒ 123 456 789 3 ∗ 3 AT ⇒ 147 258 369 3 ∗ 3
• 8. TYPES OF MATRIX 9. Symmetric Matrices - A square matrices A is called symmetric matrices if it is equal to its transpose e.g.-𝐴 ⇒ 100 010 001 3 ∗ 3, 𝐴′ ⇒ 100 010 001 3 ∗ 3 10.Equal Matrices – If two matrices order and there corresponding element is same is called equal matrices If X⇒ 2 3 4 5 2 ∗ 2 𝑎𝑛𝑑 𝑌 ⇒ 2 3 4 5 2 ∗ 2
• 9. TYPES OF MATRIX 11.Algebraic Matrices – There are three type:- i. Addition method - for addition of two matrices the order must be same e.g.:- A⇒ 3 −2 1 −4 2 ∗ 2, 𝐵 ⇒ 3 −1 4 6 2 ∗ 2 𝐴 − 𝐵 ⇒ 3 −2 1 −4 + 3 −1 4 6 ⇒ 3 + 3 −2 + −1 1 + 4 −4 + 6 ⇒ 6 −3 5 2 2 ∗ 2
• 10. TYPES OF MATRIX ii. Subtraction method –For subtraction of two matrices the order must be same. Example:- A⇒ 3 2 1 6 2 3 4 8 9 3 ∗ 3, 𝐵 ⇒ 5 6 −2 1 −2 −3 3 4 7 3 ∗ 3 A-B⇒ 3 2 1 6 2 3 4 8 9 − 5 6 −2 1 −2 −3 3 4 7 ⇒ 3 − 5 2 − 6 1 − −2 6 − 1 2 − −2 3 − −3 4 − 3 8 − 4 9 − 7 ⇒ −2 −4 3 5 4 6 1 4 2
• 11. TYPES OF MATRIX iii. Multiplication of method – Example:- and Then,
• 12. TYPES OF MATRIXLet, and Compute AB. Solution: The size of matrix A is 2x3, and the size of matrix B is 3x3. Since the number of columns of matrix A is equal to the number of rows of matrix B, the matrix product C = AB is defined. Furthermore, the size of matrix C is 2x3. Thus,
• 13. TYPES OF MATRIX It remains now to determine the entries c11, c12, c13, c21, c22 and c23. We have So the required product AB is given by
• 14. ACTION OF MATRIX Matrix Multiplication in Economics We gave you an example of how matrix multiplication could be used in math itself, but how about in real life, what benefit can it provide to us? Well, The basic principle for the example concerns the cost of producing several units of an item when the cost per unit is known. {Number of units} * {Cost per unit} = {Total cost} Example A company manufactures two products. For \$ 1.00 worth of product A, the company spends \$ .40 on materials, \$.20 on labor, and \$.10 on overhead. For \$1.00 worth of product B, the company spends \$.30 on materials, \$.25 on labor, and \$.35 on overhead. Suppose the company wishes to manufacture x1 dollars worth of product A and B. Give a vector that describes the various costs the company will have to endure?
• 15. ACTION OF MATRIX Step 1 .40 .30 A = .20 and B = .25 .10 .35 Step 2 The cost of manufacturing x1 dollars worth of A are given by x1*A and the costs of manufacturing x2 dollars worth of B are given by x2.B. Hence the total costs for both products are simply given by their products once again, .40 .30 [ x1 ] .20 + [ x2 ] .25 = x1*A + x2*B. .10 .35
• 16. ACTION OF MATRIX In geology, matrices are used for taking seismic surveys. They are used for plotting graphs, statistics and also to do scientific studies in almost different fields. • Matrices are used in representing the real world data’s like the traits of people’s population, habits, etc. They are best representation methods for plotting the common survey things. • Matrices are used in calculating the gross domestic products in economics which eventually helps in calculating the goods production efficiently. • Matrices are used in many organizations such as for scientists for recording the data for their experiments. • In robotics and automation, matrices are the base elements for the robot movements. The movements of the robots are programmed with the calculation of matrices’ rows and columns. The inputs for controlling robots are given based on the calculations from matrices.
• 17. conclution  Matrices are nothing but the rectangular arrangement of numbers, expressions, symbols which are arranged in columns and rows.  The numbers present in the matrix are called as entities or entries.  A matrix is said to be having ‘m’ number of rows and ‘n’ number of columns.  Matrices find many applications in scientific fields and apply to practical real life problems as well, thus making an indispensable concept for solving many practical problems.
• 18. Thank you! MATRIX AND IT'S BUSINESS APPLICATION