UNIT-7-OBJECTIVE 1- DETERMINANTS; EXPANSION BY MINORS

		There are several ways to find the value of a 3*3 determinant. One way to find
		the value of a determinant is to expand a determinant by minors. In general, the
		minor of an element in a 3*3 determinant is the 2*2 determinant that is found 
		by eliminating the row and column that contain that element. The signs for the 
		expansion of a 3*3 determinant by minors is
			

		The value of the determinant is the sum of the products of the elements in the
		choosen row and column, each with the appropriate  sign and their minors.

		Example 1
			

		You can expand by any row or column. We'll expand using elements in the second
		row and their minors.
			
		Sign of the element
			
		If we expand by third column we would get the following :


		Expansion by minor can be used with any determinant of order three or greater.


		Determinants can be used to solve systems of equations. To solve 3 equations and
		3 unknowns the denominator for all three variables is the determinant of the
		coefficient of these variables which is a 3*3 determinant. For each variables
		numerator replace the coefficients for that variable with the constants on the
		right of the equations.

		Example2


		We can substitute the value for x and y into any of the original equation to 
		solve for z or we can evaluate the determinant.
		(Choosing the first equation)



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