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Introduction |
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It is a rectangular array of numbers, arranged in rows and columns. |
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The number of rows (say m) and the number of columns (say n) determine the order of the matrix. It is written as m x n (to be read as m by n). |
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The plural of matrix is matrices. Matrix is usually denoted by capital letters such as A, B, C,… |
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The Types of Matrices are: square matrix, row matrix, column matrix, zero matrix or a null matrix. |
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Equality of Matrices |
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If two matrices have their corresponding elements equal, then they are called equal matrices. |
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Two equal matrices are exactly the same.
If the given matrix A is of the order m x n, then its transpose will be of the order n x m. |
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Addition of Matrices |
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To add two matrices: |
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(i) Check whether they are of the same order. |
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(ii) If they are of the same order, add the corresponding elements. |
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(ii) It will be seen that the matrix obtained after addition will also be a matrix of the same order. |
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Subtraction of Matrices |
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Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add them. |
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Multiplication of a Matrix by a Scalar |
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When a matrix is multiplied by a scalar factor k, then each element of the matrix is multiplied by k. |
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Some properties of Addition and Subtraction of Matrices |
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The Properties of Matrices are: Commutative property, Distributive property, Associative property, additive inverse property. Zero matrix possesses identity property of addition. |
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Multiplication of Matrices |
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Two matrices A and B can be multiplied if the number of columns of A is equal to the number of rows of B. The resultant matrix will be of the order of (number of rows of A x number of columns of B). |
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If A be a matrix of the order m x n and B be a matrix of the order n x q, then A and B can be multiplied and the product will be a matrix of order m x q. |
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Elements of rows of matrix A are multiplied by the corresponding elements of columns of B and we get AB. |
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Summary |
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1. A matrix is a rectangular array of numbers, arranged in rows and columns. |
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2. Order of a matrix = Number of rows in it x Number of columns in it |
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3. Row matrix is a matrix with only one row. |
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4. Column matrix is a matrix with only one column. |
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5. Zero or Null matrix is a matrix in which every element is zero.
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