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Basic Concepts Of Determinant Part 2

Posted on - 04-01-2017

Math

IIT JEE

Product of two Determinants

We can write

Here we have multiplied rows by rows. We can also multiply rows by columns or columns by rows, or columns by columns.

Note:

If D = |aij| is a determinant of order n, then the value of the determinant |Aij|, where Aij is the cofactor of aij, is Dn-1. This is known as power cofactor formula. .

Example.1

Prove the following by multiplication of determinants and power co-factor formula.

=

Solution

(i) First determinant is equal to ( 2abc)2

(ii) Second determinant is direct multiplication of determinants in row to row . .

(iii) Third determinant is co-factors of the first determinant and therefore square of the first.

Example.2

For all values of A,B,C and P,Q,R, show that

Solution:

The given determinant is equal to

 
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