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VINOD A V,

PGT Mathematics,

Jawahar Navodaya Vidyalaya,

Thrissur-KERALA

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Properties of Determinants

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For any square matrix A, |A| satisfies the following properties.

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Solution

 

 

 

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Application of Determinants

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Find the area of the triangle with vertices P(5, 4), Q(–2, 4) and R(2, –6)

Let A be the area of the triangle PQR, then

 

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Condition of collinearity of three points :

 

 

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Equation of a line passing through the given two points

 

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Show that points (a, b + c), (b, c + a) and (c, a + b) are collinear.

 

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Find equation of the line joining A(1, 3) and B(2, 1) using determinants.

Let P(x, y) be any point on the line joining A(1, 3) and B(2, 1). Then

 

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Singular Matrix

 

 

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ADJOINT OF A SQUARE MATRIX

 

Adjoint of a Square matrix of Order 2

 

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Adjoint of a Square matrix of Order 2

 

Example

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Theorem:

 

Verification

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INVERSE OF A MATRIX

 

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Properties of Inverse

 

Hence a square matrix A is invertible if and only if A is non-singular.

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  • Every invertible matrices posses a unique inverse

 

 

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SOLUTION OF A SYSTEM OF LINEAR EQUATIONS