Determinant of a matrix of order Three
Determinant 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 a row or a column . There are 6 ways of expanding a determinant of order 3 corresponding to each of 3 rows ( R1 , R2 and R3 ) and 3 columns ( C1 , C2 and C3 ).
o Expansion along first Row ( R1 ) o Expansion along second Row ( R2 ) o Expansion along third Row ( R3 ) o Expansion along first Column ( C1 ) o Expansion along second Column ( C2 ) o Expansion along third Column ( C3 )
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For easier calculations , we shall expand the determinant along that row or column which contains maximum number of zeros .
While expanding , instead of multiplying by (– 1 ) i + j , we can multiply by + 1 or – 1 according as ( i + j ) is even or odd
Numerical : Determine determinant of the matrix
Solution : Determinant of this matrix = ( 2 x -1 ) – ( 4 x -5 ) = 18
Numerical : Determine determinant of the matrix