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