Using cofactors of elements of third column, evaluate:
$increment space equals space open vertical bar table row 1 cell space space straight x end cell cell space space yz end cell row 1 cell space space straight y end cell cell space space zx end cell row 1 cell space space straight z end cell cell space space xy end cell end table close vertical bar.$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

increment space equals space open vertical bar table row 1 cell space space straight x end cell cell space space yz end cell row 1 cell space space straight y end cell cell space space zx end cell row 1 cell space space straight z end cell cell space space xy end cell end table close vertical bar

straight A subscript 13 space equals space left parenthesis negative 1 right parenthesis to the power of 1 plus 3 end exponent space open vertical bar table row 1 cell space space space space straight y end cell row 1 cell space space space space straight z end cell end table close vertical bar space equals space 1 left parenthesis straight z minus straight y right parenthesis space equals space straight z minus straight y straight A subscript 23 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 3 end exponent open vertical bar table row 1 cell space space space straight x end cell row 1 cell space space space straight z end cell end table close vertical bar space equals space minus left parenthesis straight z minus straight x right parenthesis space equals space straight x minus straight z straight A subscript 33 space equals space left parenthesis negative 1 right parenthesis to the power of 3 plus 3 end exponent space open vertical bar table row 1 cell space space space straight x end cell row 1 cell space space straight y end cell end table close vertical bar space equals space 1 left parenthesis straight y minus straight x right parenthesis space equals space straight y minus straight x

Now comma space increment space equals space straight a subscript 13 straight A subscript 13 plus straight a subscript 23 straight A subscript 23 plus straight a subscript 33 straight A subscript 33 space space space space space equals space yz left parenthesis straight z minus straight y right parenthesis plus zx left parenthesis straight x minus straight z right parenthesis plus xy left parenthesis straight y minus straight x right parenthesis space space space space space equals space yz squared minus straight y squared straight z plus zx squared minus straight z squared straight x plus xy squared minus straight x squared straight y space space space space space equals space left parenthesis xy squared minus xz squared right parenthesis plus left parenthesis yz squared minus yx squared right parenthesis plus left parenthesis zx squared minus zy squared right parenthesis space space space space space space equals straight x left parenthesis straight y squared minus straight z squared right parenthesis space plus straight y left parenthesis straight z squared minus straight x squared right parenthesis space plus space straight z left parenthesis straight x squared minus straight y squared right parenthesis therefore space space space space space increment space equals 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 thin space space space space open square brackets because space sum from blank to blank of straight a space left parenthesis straight b squared minus straight c squared right parenthesis space equals space left parenthesis straight a minus straight b right parenthesis thin space left parenthesis straight b minus straight c right parenthesis thin space left parenthesis straight c minus straight a right parenthesis space close square brackets

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

Loaction