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Matrices
 

Matrices

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matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.

It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.

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    Matrices Matrices Presentation Transcript

    • MATRICES Presented By, Neelam H. Wadhwani Amruta D. Shrirao tqma2z.blogspot.com
    • WHAT IS MEANT BY MATRIX?
      • A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.
    • TYPES OF MATRICES
      • 1 . RECTANGULAR MATRIX
      • 2. SQUARE MATRIX
      • 3. ROW AND COLUMN MATRIX
      • 4. DIAGONAL MATRIX
      • 5. SCALAR MATRIX
      • 6. UNIT MATRIX
      • 7. ZERO MATRIX
    • OPERATION OF MATRICES
      • 1. EQUALITY OF MATRICES
      • 2. ADDITION OF MATRICES
      • 3. SUBTRACTING OF MATRICES
      • 4. MULTIPLICATION OF MATRICES
      • 1. EQUALITY OF MATRICES: Two matrices are said to be equal if they have the same order and all the corresponding elements are equal.
      • 2. ADDITION OF MATRICES: The sum of two matrices of the same order is the matrix whose element are the sum of the corresponding elements of the given matrices.
      • 3. SUBTRACTING OF MATRICES: Subtraction of the matrices is also done in the same manner of addition of matrices. When the matrix B is to be subtracted from matrix A, the elements in a matrix B are subtracted from corresponding elements in matrix A.
      • 4. MULTIPLICATION OF MATRICES: A matrix may be multiplied by any number or any other matrix. Multiplication of a matrix by any one number is called a scalar multiplication.
    • PROPERTIES OF MATRIX MULTIPLICATION
      • 1. Matrix multiplication is associative: If A, B and C are three matrices, and AB, BC are defined then
      • A(BC)=(AB)C
      • 2. Matrix multiplication is distributive: If A, B and C are three matrices of proper order then
      • A(B+C)=AB+AC and (B+C)A=BA+CA
      • 3. Matrix multiplication is in general, not commutative: If A & B are two matrices such that AB and BA are defined, then AB is not equal to BA in general.
    • TRANSPOSE OF A MATRIX
      • The matrix obtained by interchanging the rows and columns of a matrix is called transpose of a matrix. The transpose of a matrix A is denoted by A’.
    •