Question

$Let space straight A equals space open square brackets table row 2 cell space 3 end cell row cell negative 1 end cell cell space 2 end cell end table close square brackets space and space straight f space left parenthesis straight x right parenthesis space equals space straight x squared minus 4 straight x plus 7 space show space that space straight f left parenthesis straight A right parenthesis space equals space straight O. space use space this space result space to space find space straight A to the power of 5$

Solution

we space have space comma space straight f left parenthesis straight x right parenthesis equals straight x squared minus 4 straight x plus 7 therefore space space straight f space left parenthesis straight A right parenthesis equals space straight A squared space minus 4 straight A space plus space 7 space straight I subscript 2 space Now space space space straight A equals space open square brackets table row 2 cell space space 3 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space space space space space space space space space space straight A squared space space equals space open square brackets table row 2 cell space space 3 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space open square brackets table row 2 cell space space 3 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space space space space equals space space open square brackets table row cell 4 minus 3 end cell cell space space space space space space space 6 plus 6 end cell row cell negative 2 minus 2 end cell cell space space minus 3 plus 4 end cell end table close square brackets equals space open square brackets table row 1 cell space space 12 end cell row cell negative 4 end cell cell space space 1 end cell end table close square brackets space space space space space space space space minus 4 straight A space equals space open square brackets table row cell negative 8 end cell cell space space minus 12 end cell row 4 cell space minus 8 end cell end table close square brackets space and space 7 space straight I subscript 2 space equals space open square brackets table row 7 cell space space 0 end cell row 0 cell space space 7 end cell end table close square brackets therefore space space space space straight f space left parenthesis straight A right parenthesis space equals space straight A squared minus 4 straight A plus 7 space straight I subscript 2 rightwards double arrow space space space space straight f space left parenthesis straight A right parenthesis space equals space open square brackets table row 1 cell space space 12 end cell row cell negative 4 end cell cell space 1 end cell end table close square brackets plus space open square brackets table row cell negative 8 end cell cell space space minus 12 end cell row 4 cell space minus 8 end cell end table close square brackets space plus space open square brackets table row 7 cell space space 0 end cell row 0 cell space space 7 end cell end table close square brackets rightwards double arrow space space space space straight f space left parenthesis straight A right parenthesis space equals space open square brackets table row cell 1 minus 8 plus 7 end cell cell 12 minus 12 plus 0 end cell row cell negative 4 plus 4 plus 0 end cell cell 1 minus 8 plus 7 end cell end table close square brackets equals space open square brackets table row 0 cell space space 0 end cell row 0 cell space space 0 end cell end table close square brackets equals straight O Now comma space space space space space space space straight f space left parenthesis straight A right parenthesis space equals straight O rightwards double arrow space space space straight A squared space minus 4 straight A plus 7 straight I subscript 2 space equals 0 space space space... left parenthesis 1 right parenthesis rightwards double arrow space space space straight A squared space minus 4 straight A plus 7 straight I subscript 2 rightwards double arrow space space space straight A cubed minus 4 straight A squared plus 7 straight I subscript 2 space straight A rightwards double arrow space space space straight A cubed minus 4 left parenthesis 4 straight A plus 7 straight I subscript 2 space right parenthesis minus 7 straight A space space space space space space open square brackets table row cell because space of end cell cell left parenthesis 1 right parenthesis end cell end table close square brackets rightwards double arrow space space space straight A cubed minus 9 straight A plus 282 straight I subscript 2 space rightwards double arrow space space space straight A cubed minus 9 straight A squared minus 28 straight A space equals space 9 space left parenthesis 4 straight A minus space 7 space straight I subscript 2 space right parenthesis space minus 28 straight A space space open square brackets table row cell because space of end cell cell left parenthesis 1 right parenthesis end cell end table close square brackets rightwards double arrow space space space straight A cubed minus 36 straight A minus 63 straight I subscript 2 space minus space 28 space straight A equals space 8 straight A minus 63 space straight I subscript 2 rightwards double arrow space space space straight A cubed minus 8 straight A squared minus 63 straight A rightwards double arrow space space space straight A to the power of 5 equals 8 left parenthesis 4 straight A minus 7 straight I subscript 2 right parenthesis minus 63 straight A equals space minus 31 straight A minus 56 space straight I subscript 2 rightwards double arrow space space space straight A to the power of 5 minus 31 space open square brackets table row 2 3 row 1 2 end table close square brackets minus 56 space open square brackets table row 1 cell space 0 end cell row 0 cell space space 1 end cell end table close square brackets rightwards double arrow space space space straight A to the power of 5 space equals space open square brackets table row cell negative 62 end cell cell negative 93 end cell row 31 cell negative 62 end cell end table close square brackets plus space open square brackets table row cell negative 56 end cell cell space space 0 end cell row 0 cell space space minus 56 end cell end table close square brackets space space space rightwards double arrow space space space straight A to the power of 5 space equals open square brackets table row cell negative 118 end cell cell space minus 93 end cell row 31 cell space space minus 118 end cell end table close square brackets space

For Daily Free Study Material Join wiredfaculty

Matrices

Some More Questions From Matrices Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction