Without expanding, prove that $open vertical bar table row cell straight x plus straight y end cell cell space space straight x end cell cell space space space straight x end cell row cell 5 straight x plus 4 straight y end cell cell space space 4 straight x end cell cell space space space space 2 straight x end cell row cell 10 straight x plus 8 straight y end cell cell space space 8 straight x end cell cell space space space space 3 straight x end cell end table close vertical bar space equals space x cubed$

Solution

Let space space increment space equals space open vertical bar table row cell straight x plus straight y end cell cell space space straight x end cell cell space space space straight x end cell row cell 5 straight x plus 4 straight y end cell cell space space 4 straight x end cell cell space space space space 2 straight x end cell row cell 10 straight x plus 8 straight y end cell cell space space 8 straight x end cell cell space space space space 3 straight x end cell end table close vertical bar space space space space space space space space space space space space space space equals space open vertical bar table row straight x straight x cell space straight x end cell row cell 5 straight x end cell cell 4 straight x end cell cell space space 2 straight x end cell row cell 10 straight x end cell cell 8 straight x end cell cell space 3 straight x end cell end table close vertical bar space plus space open vertical bar table row straight y straight x cell space straight x end cell row cell 5 straight y end cell cell 4 straight x end cell cell space space 2 straight x end cell row cell 10 straight y end cell cell 8 straight x end cell cell space 3 straight x end cell end table close vertical bar space space space space space space space space space space space space space equals space straight x cubed space open vertical bar table row 1 cell space 1 end cell cell space space 1 end cell row 5 cell space 4 end cell cell space space 2 end cell row 10 cell space 8 end cell cell space 3 end cell end table close vertical bar space plus straight x squared space straight y space space open vertical bar table row 1 cell space space 1 end cell cell space 1 end cell row 4 cell space space 4 end cell cell space space 2 end cell row 8 cell space space 8 end cell cell space 3 end cell end table close vertical bar space space space space space space space space space space space space space equals space space straight x cubed space open vertical bar table row 1 cell space space space space 0 end cell cell space space 0 end cell row 5 cell space minus 1 end cell cell space space 3 end cell row 10 cell space minus 2 end cell cell space space 7 end cell end table close vertical bar space plus straight x squared space straight y space left parenthesis 0 right parenthesis space space space space space space space space space space space space space equals space space straight x cubed space open vertical bar table row 1 cell space space space space space space 0 end cell cell space space space space space 0 end cell row 5 cell space space minus 1 end cell cell space space minus 3 end cell row 0 cell space space space space space space 0 end cell cell space minus 1 end cell end table close vertical bar space plus space 0 equals straight x to the power of 3 space end exponent space space open vertical bar table row 1 cell space space space space space space 0 end cell cell space space space space space 0 end cell row 5 cell space space minus 1 end cell cell space space minus 3 end cell row 0 cell space space space space space space 0 end cell cell space minus 1 end cell end table close vertical bar space space space space space space space space space space space space space equals space space straight x cubed space open vertical bar table row 1 cell space space space space space space 0 end cell cell space space space space space 0 end cell row 5 cell space space minus 1 end cell cell space space minus 3 end cell row 0 cell space space space space space space 0 end cell cell space minus 1 end cell end table close vertical bar space comma space by space straight R subscript 2 minus 5 space straight R subscript 1 space space space space space space space space space space space space space equals space space straight x cubed space open square brackets table row cell left parenthesis 1 right parenthesis left parenthesis negative 1 right parenthesis left parenthesis negative 1 right parenthesis end cell end table close square brackets space space space space open square brackets table row cell product space of space diagonal space element space end cell end table close square brackets space space space space space space space space space space space space space equals space space straight x cubed space space space space space space space space space space space space space space space space space space space space space space space space space

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