Slide 1 : DETERMINANTS
Slide 2 : we have studied about matrices and algebra of matrices. We have also learnt that a system of algebraic equations can be expressed in the form of matrices. This means, a system of linear equations like
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Determinant of a matrix of order 3 × 3Determinant of a matrix of order three can be determined by expressing it in terms of second order determinants. This is known as expansion of a determinant along row (or a column). : Determinant of a matrix of order 3 × 3Determinant of a matrix of order three can be determined by expressing it in terms of second order determinants. This is known as expansion of a determinant along row (or a column).
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Slide 12 : Properties of Determinants
In the previous section, we have learnt how to expand the determinants. In this section,
we will study some properties of determinants which simplifies its evaluation by obtaining
maximum number of zeros in a row or a column.
These properties are true for determinants of any
order. However, we shall restrict ourselves up to
determinants of order 3 only.
Slide 13 : Property 1 The value of the determinant remains unchanged if its rows and columns are interchanged.
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Slide 17 : Property 3 If any two rows (or columns) of a determinant are identical (all corresponding
elements are same), then value of determinant is zero.
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