Question

Write the minors and cofactors of the elements of following determinants:
$open vertical bar table row 1 cell space space space 0 end cell 4 row 3 cell space space 5 end cell cell negative 1 end cell row 0 cell space 1 end cell cell space 2 end cell end table close vertical bar$

Solution

Let $increment space equals space open vertical bar table row 1 cell space space space space 0 end cell cell space space space 4 end cell row 3 cell space space 5 end cell cell space minus 1 end cell row 0 cell space 1 end cell cell space space space 2 end cell end table close vertical bar$
$straight M subscript 11 space space equals space open vertical bar table row 5 cell space space minus 1 end cell row 1 cell space space space space space 2 end cell end table close vertical bar space equals space 10 plus 1 space equals space 11 comma space space straight A subscript 11 space equals space left parenthesis negative 1 right parenthesis to the power of 1 plus 1 end exponent straight M subscript 11 space equals space straight M subscript 11 space equals space 11 straight M subscript 12 space equals space open vertical bar table row 3 cell space space space space minus 1 end cell row 0 cell space space space space space space 2 end cell end table close vertical bar space equals space 6 minus 0 space equals space 6 comma 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 straight M subscript 12 space equals space minus 6 straight M subscript 13 space equals space open vertical bar table row 3 cell space space space space 5 end cell row 0 cell space space space space 1 end cell end table close vertical bar space equals space 3 minus 0 space equals space 3 comma space space straight A subscript 13 space equals space left parenthesis negative 1 right parenthesis to the power of 1 plus 3 end exponent space straight M subscript 13 space equals space straight M subscript 13 space equals space 3 straight M subscript 21 space equals space space open vertical bar table row 0 cell space space space space 4 end cell row 1 cell space space space space 2 end cell end table close vertical bar space equals space 0 minus 4 space equals space minus 4 comma 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 straight M subscript 21 space equals space 4 straight M subscript 22 space equals space open vertical bar table row 0 cell space space space space space 4 end cell row 1 cell space space space space space 2 end cell end table close vertical bar space equals space 0 minus 4 space equals space minus 4 comma 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 straight M subscript 22 space equals space minus 4 straight M subscript 23 space equals space open vertical bar table row cell 1 space end cell cell space space space 0 end cell row 0 cell space space space 1 end cell end table close vertical bar space equals space 1 minus 0 space equals space 1 comma 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 straight M subscript 23 space equals space minus 1 straight M subscript 31 space equals space open vertical bar table row 0 cell space space space space space space space 4 end cell row 5 cell space space space minus 1 end cell end table close vertical bar space equals space 0 minus 20 space equals space minus 20 comma space space straight A subscript 31 space equals space left parenthesis negative 1 right parenthesis to the power of 3 plus 1 end exponent straight M subscript 31 space equals space straight M subscript 31 space equals space minus 20 straight M subscript 32 space equals space open vertical bar table row 1 cell space space space space space space space space 4 end cell row 3 cell space space space space space space minus 1 end cell end table close vertical bar space equals space minus 1 minus 12 space equals space minus 13 comma 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 straight M subscript 32 space equals space 13 straight M subscript 33 space equals space open vertical bar table row 1 cell space space space 0 end cell row 3 cell space space space 5 end cell end table close vertical bar space equals space 5 minus 0 space equals space 5 comma 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 straight M subscript 33 space equals space 5$

For Daily Free Study Material Join wiredfaculty

Determinants

Write the minors and cofactors of the elements of following determinants:
$open vertical bar table row 1 cell space space space 0 end cell 4 row 3 cell space space 5 end cell cell negative 1 end cell row 0 cell space 1 end cell cell space 2 end cell end table close vertical bar$

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction