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CBSE Class 12-science Answered

How to solve determinants without expanding.      FOR EX.
Asked by rahulyadavkarira | 29 Mar, 2019, 09:37: PM
Expert Answer
We need to use the properties of determinants to get the value of determinent without expanding it.
Some of the properties are given below.
 
(1) If any two rows or columns are identical, then determinant value is zero.
 
(2) If each element of a row or column is multiplied by a constant k, then its determinant value is multiplied by same k.
       Using this property if there is a common factors in a row or column, this can be factored out.
       Also if elements of row or column or respectively proportional to each other, determinant value is zero.
 
(3) If to each elemnt of any row or column, the equimultiples of corresponding elements of other row or column are added,
     then the value of determinant remains same
 
example :-  prove    D = begin mathsize 12px style open vertical bar table row 2 7 65 row 3 8 75 row 5 9 86 end table close vertical bar end style = 0
 
C3+C1 →  D = begin mathsize 12px style open vertical bar table row 2 7 72 row 3 8 83 row 5 9 95 end table close vertical bar end style  ;     C3 - C1 →  D = begin mathsize 12px style open vertical bar table row 2 7 70 row 3 8 80 row 5 9 90 end table close vertical bar end style  ;   C3/10 → begin mathsize 12px style 10 space open vertical bar table row 2 7 7 row 3 8 8 row 5 9 9 end table close vertical bar space equals space 0 space space space because space e l e m e n t s space C 2 space a n d space C 3 space a r e space i d e n t i c a l end style
Answered by Thiyagarajan K | 31 Mar, 2019, 10:07: AM

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