+91-8076753736[email protected]
logo
logo
-->

Determinants

Question
CBSEENMA12034550
Wired Faculty App

Verify A(adj A) = (adj A) A = | A | 1 for the matrix
straight A space equals space open square brackets table row 1 cell space space space space 1 end cell cell space space space space space space 2 end cell row 3 cell space space space space 0 end cell cell space space minus 2 end cell row 1 cell space space space space 0 end cell cell space space space space space 3 end cell end table close square brackets.

Solution
Let space straight A space equals space open square brackets table row 1 cell space space space space space 1 end cell cell space space space space 2 end cell row 3 cell space space space space space 0 end cell cell space space minus 2 end cell row 1 cell space space space space 0 end cell cell space space space space 3 end cell end table close square brackets
therefore space space space open vertical bar straight A close vertical bar space equals space open vertical bar table row 1 cell space space space 1 end cell cell space space space space space 2 end cell row 3 cell space space space space 0 end cell cell space space minus 2 end cell row 1 cell space space space 0 end cell cell space space space space space 3 end cell end table close vertical bar therefore space space straight A subscript 11 space equals space left parenthesis negative 1 right parenthesis to the power of 1 plus 1 end exponent thin space straight M subscript 11 space equals space open vertical bar table row 0 cell space space space minus 2 end cell row 0 cell space space space space space space 3 end cell end table close vertical bar space equals space 0 comma space space space space space space space straight A subscript 12 space equals space left parenthesis negative 1 right parenthesis to the power of 1 plus 2 end exponent straight M subscript 12 space equals space minus open vertical bar table row 3 cell space space space space minus 2 end cell row 1 cell space space space space space space 3 end cell end table close vertical bar space equals space minus left parenthesis 9 plus 2 right parenthesis space equals space minus 11 space space space space space space space straight A subscript 13 space equals space left parenthesis negative 1 right parenthesis to the power of 1 plus 3 end exponent straight M subscript 13 space equals space open vertical bar table row 3 cell space space space space 0 end cell row 1 cell space space space space space 0 end cell end table close vertical bar space equals space 0 comma space space space space space space space straight A subscript 21 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 1 end exponent straight M subscript 21 space equals space minus open vertical bar table row 1 cell space space space 2 end cell row 0 cell space space 3 end cell end table close vertical bar space equals space minus 3 space space space space space space straight A subscript 22 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 2 end exponent straight M subscript 22 space equals space open vertical bar table row 1 cell space space space space 2 end cell row 1 cell space space space space 3 end cell end table close vertical bar space equals space 3 minus 2 space equals space 1 space space space space space straight A subscript 23 space equals space left parenthesis negative 1 right parenthesis to the power of 2 plus 3 end exponent straight M subscript 23 space equals space minus open vertical bar table row 1 cell space space space space 1 end cell row 1 cell space space space space 0 end cell end table close vertical bar space equals space minus left parenthesis negative 1 right parenthesis space equals space 1 space space space space straight A subscript 31 space equals space left parenthesis negative 1 right parenthesis to the power of 3 plus 1 end exponent space straight M subscript 31 space equals space open vertical bar table row 1 cell space space space space space space 2 end cell row 0 cell space space minus 2 end cell end table close vertical bar space equals space minus 2 comma space space space space straight A subscript 32 space equals space left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent straight M subscript 32 space equals space minus open vertical bar table row 1 cell space space space space space space 2 end cell row 3 cell space space minus 2 end cell end table close vertical bar space equals negative left parenthesis negative 2 minus 6 right parenthesis space equals space 8 space space space straight A subscript 33 space equals space left parenthesis negative 1 right parenthesis to the power of 3 plus 3 end exponent straight M subscript 33 space equals space open vertical bar table row 1 cell space space space 1 end cell row 3 cell space space space space 0 end cell end table close vertical bar space equals space minus 3
adj space straight A space equals open square brackets table row 0 cell space space minus 11 end cell cell space space space 0 end cell row cell negative 3 end cell cell space space space 1 end cell cell space space space 1 end cell row cell negative 2 end cell cell space space space 8 end cell cell space space space minus 3 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row 0 cell space minus 3 end cell cell space minus 2 end cell row cell negative 11 end cell cell space space space 1 end cell cell space space space 8 end cell row 0 cell space space 1 end cell cell space space minus 3 end cell end table close square brackets space space space space space space space open vertical bar straight A close vertical bar space equals space 1 cross times 0 space minus space left parenthesis 1 right parenthesis thin space left parenthesis negative 11 right parenthesis space plus 2 space cross times 0 space equals space minus 11 straight A space adj space straight A space equals space open square brackets table row 1 cell space space space minus 1 end cell cell space space space space space 2 end cell row 3 cell space space space space space 0 end cell cell space space minus 2 end cell row 1 cell space space space space space 0 end cell cell space space space space 3 end cell end table close square brackets space open square brackets table row 0 cell space minus 3 end cell cell space space minus 2 end cell row cell negative 11 end cell cell space space space space 1 apostrophe end cell cell space space space space 8 end cell row cell space space 0 end cell cell space 1 end cell cell space space minus 3 end cell end table close square brackets space space space space space space space space space space space space space space space space equals space open square brackets table row cell negative 11 end cell cell space space minus 3 plus 1 plus 2 end cell cell space space space minus 2 plus 8 minus 6 end cell row 0 cell negative 9 minus 2 end cell cell space space minus 6 plus 0 plus 6 end cell row 0 cell negative 3 plus 3 end cell cell negative 2 minus 9 end cell end table close square brackets space space space space space space space space space space space space space space space equals space open square brackets table row cell negative 11 end cell 0 cell space space space space 0 end cell row 0 cell negative 11 end cell cell space space space space 0 end cell row 0 0 cell negative 11 end cell end table close square brackets space equals space minus 11 space cross times open square brackets table row 1 cell space space 0 end cell cell space space 0 end cell row 0 cell space 1 end cell cell space 0 end cell row 0 cell space 0 end cell cell space 1 end cell end table close square brackets space space space space space space space space space space space space space space space space equals space open vertical bar straight A close vertical bar space straight I left parenthesis adj space straight A right parenthesis thin space straight A space equals space open square brackets table row cell space space space space 0 end cell cell space space minus 3 end cell cell space space minus 2 end cell row cell negative 11 end cell cell space space space 1 end cell cell space space space space space space 8 end cell row cell space space 0 end cell cell space space space 1 end cell cell space space minus 3 end cell end table close square brackets space space open square brackets table row 1 cell space space minus 1 end cell cell space space space space 2 end cell row 3 cell space space 0 end cell cell space minus 2 end cell row 1 cell space 0 end cell cell space 3 end cell end table close square brackets space space space space space space space space space space space space space space space space equals space open square brackets table row cell 0 minus 9 minus 2 end cell cell space space 0 plus 0 plus 0 end cell cell space space 0 plus 6 minus 6 end cell row cell negative 11 plus 3 plus 8 end cell cell space space space minus 11 plus 0 plus 0 end cell cell space space minus 22 minus 2 plus 24 end cell row cell 0 plus 3 minus 3 end cell cell space space space 0 plus 0 plus 0 end cell cell space space 0 minus 2 minus 9 end cell end table close square brackets space space space space space space space space space space space space space space space space equals open square brackets table row cell negative 11 end cell cell space space space 0 end cell 0 row 0 cell negative 11 end cell 0 row 0 cell space 0 end cell cell negative 11 end cell end table close square brackets space equals space minus 11 open square brackets table row 1 cell space space space 0 end cell cell space 0 end cell row 0 cell space space 1 end cell cell space 0 end cell row 0 cell space space 0 end cell cell space 1 end cell end table close square brackets space space space space space space space space space space space space space space space equals open vertical bar straight A close vertical bar space straight I therefore space straight A space adj space straight A space equals space left parenthesis adj space straight A right parenthesis space equals open vertical bar straight A close vertical bar space straight I

Some More Questions From Determinants Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation