Matrices
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Transcript of Matrices
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MATRICES
Presented By,
Neelam H. WadhwaniAmruta D. Shriraotqma2z.blogspot.com
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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.
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TYPES OF MATRICES
1. RECTANGULAR MATRIX2. SQUARE MATRIX3. ROW AND COLUMN MATRIX4. DIAGONAL MATRIX5. SCALAR MATRIX6. UNIT MATRIX7. ZERO MATRIX
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OPERATION OF MATRICES
1. EQUALITY OF MATRICES2. ADDITION OF MATRICES3. SUBTRACTING OF MATRICES4. MULTIPLICATION OF MATRICES
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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.
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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.
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PROPERTIES OF MATRIX MULTIPLICATION1. 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
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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.
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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’.
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