Question

For what value of ‘a’ is the matrix
$open square brackets table row 4 cell space minus 3 end cell cell space space space space space minus 1 end cell row 2 cell space space space space space straight a end cell cell space space space space space space space space 6 end cell row 3 cell space space minus 5 end cell cell space space space minus 4 end cell end table close square brackets$
singular?

Solution

Let $straight A space equals open square brackets table row 4 cell space minus 3 end cell cell space space space space space minus 1 end cell row 2 cell space space space space space straight a end cell cell space space space space space space space space 6 end cell row 3 cell space space minus 5 end cell cell space space space minus 4 end cell end table close square brackets$
$therefore space space open vertical bar straight A close vertical bar space equals space open vertical bar table row 4 cell space minus 3 end cell cell space space minus 1 end cell row 2 cell space space space space space straight a end cell cell space space space space space space 6 end cell row 3 cell space space minus 5 end cell cell space space space minus 4 end cell end table close vertical bar space space space space space space space space space space space space equals space 4 open vertical bar table row cell space space space straight a end cell cell space space space space space space space 6 end cell row cell negative 5 end cell cell space space space minus 4 end cell end table close vertical bar minus left parenthesis negative 3 right parenthesis space open vertical bar table row 2 cell space space space space space space 6 end cell row 3 cell space space minus 4 end cell end table close vertical bar plus left parenthesis negative 1 right parenthesis thin space open vertical bar table row 2 cell space space space space space space space space straight a end cell row 3 cell space space space space minus 5 end cell end table close vertical bar space space space space space space space space space space space space equals 4 left parenthesis negative 4 straight a plus 30 right parenthesis plus 3 left parenthesis negative 8 minus 18 right parenthesis minus left parenthesis negative 10 minus 3 straight a right parenthesis space space space space space space space space space space space space equals negative 16 straight a plus 120 minus 78 plus 10 plus 3 straight a equals negative 13 straight a plus 52 For space straight A space be space to space singular comma space we space have space space space open vertical bar straight A close vertical bar space equals space 0 space space space space space space space space space rightwards double arrow space space space space space space minus 13 straight a space plus space 52 space equals space 0 space space space space space rightwards double arrow space space space 13 space straight a space equals space 52 space space space space rightwards double arrow space space space straight a space equals space 4$

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