Find the inverse of the matrix
$straight A space equals space open square brackets table row cell negative 1 end cell cell space space 1 end cell cell space space 2 end cell row cell space space space 3 end cell cell negative 1 end cell cell space space 1 space end cell row cell space minus 1 end cell cell space space 3 end cell cell space 4 end cell end table close square brackets.$

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

Solution

straight A space equals space open square brackets table row cell negative 1 end cell cell space space 1 end cell cell space space space space 2 end cell row cell space space 3 end cell cell negative 1 end cell cell space space space 1 end cell row cell negative 1 end cell cell space space 3 end cell cell space space 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 cell negative 1 end cell cell space space 1 end cell cell space space 2 end cell row 3 cell space minus 1 end cell cell space space 1 end cell row cell negative 1 end cell 3 cell space space 4 end cell end table close vertical bar space equals space left parenthesis negative 1 right parenthesis space open vertical bar table row cell negative 1 end cell cell space space 1 end cell row cell space 3 end cell cell space space 4 end cell end table close vertical bar minus 1 space open vertical bar table row 3 cell space space 1 end cell row cell negative 1 end cell cell space space 4 end cell end table close vertical bar space plus space 2 space open vertical bar table row 3 cell space minus 1 end cell row cell negative 1 end cell cell space space space space 3 end cell end table close vertical bar space space space space space space space space space space space equals space minus left parenthesis 4 minus 3 right parenthesis space minus space left parenthesis 12 plus 1 right parenthesis space plus space 2 thin space left parenthesis 9 minus 1 right parenthesis space equals space 7 minus 13 plus 16 space equals space 10 space not equal to space 0 therefore space space space space straight A to the power of negative 1 end exponent space exists. space space space space space space space space space space space straight A subscript 11 space equals space open vertical bar table row cell negative 1 end cell cell space space 1 end cell row cell space space 3 end cell cell space space 4 end cell end table close vertical bar space equals space minus 4 minus 3 space equals space minus 7 space space space space space space space space space space space straight A subscript 12 space equals space minus open vertical bar table row 3 cell space space 1 end cell row cell negative 1 end cell cell space space 4 end cell end table close vertical bar space equals negative left parenthesis 12 plus 1 right parenthesis space equals space minus 13 space space space space space space space space space space space straight A subscript 13 space equals space open vertical bar table row 3 cell space space minus 1 end cell row 1 cell space space space space 3 end cell end table close vertical bar space equals space 9 minus 1 space equals space 8 space space space space space space space space space space straight A subscript 21 space equals space minus open vertical bar table row 1 cell space space 2 end cell row 3 cell space space 4 end cell end table close vertical bar space equals space minus left parenthesis 4 minus 6 right parenthesis space equals space 2 space space space space space space space space space space straight A subscript 22 space equals space open vertical bar table row cell negative 1 end cell cell space space 2 end cell row cell negative 1 end cell cell space 4 end cell end table close vertical bar space equals space minus 4 plus 2 space equals space minus 2 space space space space space space space space space space straight A subscript 23 space equals space minus open vertical bar table row cell negative 1 end cell cell space 1 space space end cell row cell negative 1 end cell 3 end table close vertical bar space equals space minus left parenthesis negative 3 plus 1 right parenthesis space equals space 2 space space space space space space space space space space space straight A subscript 31 space equals space open vertical bar table row 1 cell space space 2 end cell row cell negative 1 end cell cell space space 1 end cell end table close vertical bar space equals space 1 plus 2 space equals space 3 space space space space space space space space space space space straight A subscript 32 space equals space minus open vertical bar table row cell negative 1 end cell cell space 2 end cell row 3 1 end table close vertical bar space equals space minus left parenthesis negative 1 minus 6 right parenthesis space equals space 7 space space space space space space space space space space space space straight A subscript 33 space equals space open vertical bar table row cell negative 1 end cell cell space space 1 end cell row 3 cell space space minus end cell end table close vertical bar space equals space 1 minus 3 space equals space minus 2

therefore space space adj. space straight A space equals space open square brackets table row cell negative 7 end cell cell negative 13 end cell cell space space 8 end cell row 2 cell negative 2 end cell cell space space 2 end cell row 3 cell space 7 end cell cell negative 2 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell negative 7 end cell cell space space 2 end cell cell space space 3 end cell row cell negative 13 end cell cell space space minus 2 end cell cell space space 7 end cell row 8 2 cell negative 2 end cell end table close square brackets space space space space space straight A to the power of negative 1 end exponent space equals space fraction numerator adj. space straight A over denominator open vertical bar straight A close vertical bar end fraction space equals space 1 over 10 open square brackets table row cell negative 7 end cell cell space space space 2 end cell cell space space space 3 end cell row cell negative 13 end cell cell space minus 2 end cell cell space space 7 end cell row 8 2 cell space minus 2 end cell end table 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