Question

Using properties of determinants, prove that:
$open vertical bar table row straight x cell space space space straight y end cell cell space space space straight z end cell row cell straight x squared end cell cell space space straight y squared end cell cell space space space straight z squared end cell row cell straight x cubed end cell cell space space straight y cubed end cell cell space space straight z cubed end cell end table close vertical bar space equals space space straight x space straight y space straight z space left parenthesis straight x minus straight y right parenthesis thin space left parenthesis straight y minus straight z right parenthesis thin space left parenthesis straight z minus straight x right parenthesis$

Solution

Let $increment equals space space open vertical bar table row straight x cell space straight y end cell cell space straight z end cell row cell straight x squared end cell cell space straight y squared end cell cell space straight z squared end cell row cell straight x cubed end cell cell space straight y cubed end cell cell space straight z cubed end cell end table close vertical bar$
$equals space straight x space straight y space straight z space open vertical bar table row 1 cell space 1 end cell cell space 1 end cell row straight x cell space straight y end cell cell space straight z end cell row cell straight x squared end cell cell space straight y squared end cell cell space straight z squared end cell end table close vertical bar equals space straight x space straight y space straight z space open vertical bar table row 1 0 cell space 0 end cell row straight x cell space straight y minus straight x end cell cell space straight z minus straight x end cell row cell straight x squared end cell cell space straight y squared minus straight x squared end cell cell space straight z squared minus straight x squared end cell end table close vertical bar comma space by space straight C subscript 2 minus straight C subscript 1 comma space space straight C subscript 3 minus straight C subscript 1 equals space straight x space straight y space straight z space open vertical bar table row cell straight y minus straight x end cell cell space space space space space space straight z minus straight x end cell row cell straight y squared minus straight x squared end cell cell space space space space space straight z squared minus straight x squared end cell end table close vertical bar comma space expanding space with space straight R subscript 1 equals space space straight x space straight y space straight z space left parenthesis straight y minus straight x right parenthesis thin space left parenthesis straight z minus straight x right parenthesis space open vertical bar table row 1 cell space space space space space space space 1 end cell row cell straight y plus straight x end cell cell space space space space straight z plus straight x end cell end table close vertical bar equals space space straight x space straight y space straight z space left parenthesis straight y minus straight x right parenthesis thin space left parenthesis straight z minus straight x right parenthesis thin space left parenthesis straight z plus straight x minus straight y minus straight x right parenthesis equals space straight x space straight y space straight z space left parenthesis straight y minus straight x right parenthesis thin space left parenthesis straight z minus straight x right parenthesis thin space left parenthesis straight z minus straight y right parenthesis equals space straight x space straight y space straight z space left parenthesis straight x minus straight y right parenthesis thin space left parenthesis straight y minus straight z right parenthesis thin space left parenthesis straight z minus straight x right parenthesis$

For Daily Free Study Material Join wiredfaculty

Determinants

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location