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| Types of Matrices |
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| A matrix having only one row is called a row-matrix. |
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| For example: A[1 3 2 -2] is a row matrix of order 1 x 4. |
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| A matrix having only one column is called a column matrix. |
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| 3 x 1 and 4 x 1 respectively. |
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| A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n. |
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| In this square matrix of order n the elements a11, a22.......ann is called the principal diagonal or the leading diagonal. |
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| The elements a11, a22,.......ann are called the diagonal elements of the square matrix. |
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| The leading diagonal elements are 2, -2 and -3. |
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| A square matrix A=[aij]nxn is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero. |
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i.e., aij = 0 for all i  j |
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| Example: |
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| A scalar matrix is a diagonal matrix in which all the diagonal elements are equal. |
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| Example: |
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The matrices  are scalar matrices of order 2 and 3 respectively. |
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| A square matrix A=[aij]n x n is called an identity or unit matrix if |
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| (2) aij =1 for all i = j |
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| In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit matrix. The identity matrix of order n is denoted by In. |
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| Example: |
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The matrices  are identify matrices
of order 2 and 3 respectively. |
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| A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O]m,n. |
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| Example: |
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 are all zero matrices of orders 1 x
2, 2 x 1, 2 x 2 and 3 x 3 respectively. |
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