For the matrix show that A 2 – 4 A + 7 I = O. Hence obtain A –1 . - Wired Faculty

Question

For the matrix $straight A space equals space open square brackets table row 2 cell space space space minus 1 end cell row 3 cell space space space space space space 2 end cell end table close square brackets comma$ show that A² – 4 A + 7 I = O. Hence obtain A^–1.

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Solution

straight A space equals space open square brackets table row 2 cell space space space space minus 1 end cell row 3 cell space space space space space space space 2 end cell end table close square brackets

therefore space space space space space space space space straight A squared space equals space open square brackets table row 2 cell space space space space minus 1 end cell row 3 cell space space space space space space space 2 end cell end table close square brackets space space open square brackets table row 2 cell space space minus 1 end cell row 3 cell space space space space space 2 end cell end table close square brackets space equals space open square brackets table row cell 4 minus 3 end cell cell space space space space minus 2 minus 2 end cell row cell 6 plus 6 end cell cell space space space space space minus 3 plus 4 end cell end table close square brackets space equals space open square brackets table row 1 cell space space space minus 4 end cell row 12 cell space space space space space 1 end cell end table close square brackets therefore space space space space space straight A squared minus 4 space straight A plus 7 space straight I space equals space open square brackets table row 1 cell space space minus 4 end cell row 12 cell space space space space 1 end cell end table close square brackets space minus space 4 space open square brackets table row 2 cell space space minus 1 end cell row 3 cell space space space space 2 end cell end table close square brackets space plus space 7 space open square brackets table row 0 cell space space space 0 end cell row 0 cell space space space 1 end cell end table close square brackets 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 space space space space space space space equals space open square brackets table row 1 cell space space space space minus 4 end cell row 12 cell space space space space space space 1 end cell end table close square brackets space space plus space space open square brackets table row cell negative 8 end cell cell space space space space space space space space 4 end cell row cell negative 12 end cell cell space space space minus 8 end cell end table close square brackets space plus space open square brackets table row 7 cell space space space space 0 end cell row 0 cell space space space space space 7 end cell end table close square brackets 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 space space space space space space space equals open square brackets table row cell 1 minus 8 plus 7 end cell cell space space space space space space space space minus 4 plus 4 plus 0 end cell row cell 12 minus 12 plus 0 end cell cell space space space space space space space space space space space space space 1 minus 8 plus 7 end cell end table close square brackets space equals space open square brackets table row 0 cell space space space space 0 end cell row 0 cell space space space space 0 end cell end table close square brackets space equals space straight O therefore space space space straight A squared minus 4 straight A plus 7 straight I space equals space straight O Now space straight A squared minus 4 straight A space plus space 7 straight I space equals straight O space space space space space space space space rightwards double arrow space space space space space 7 straight I space equals space minus straight A squared plus 4 straight A space space space space space space space rightwards double arrow space space space space 7 straight A to the power of negative 1 end exponent space equals space minus straight A plus 4 straight I rightwards double arrow space space space space space space 7 straight A to the power of negative 1 end exponent space equals negative open square brackets table row 2 cell space space space minus 1 end cell row 3 cell space space space space space space 2 end cell end table close square brackets space plus space 4 space open square brackets table row 1 cell space space space space 0 end cell row 0 cell space space space space 1 end cell end table close square brackets space equals space open square brackets table row cell negative 2 end cell cell space space space space 1 end cell row cell negative 3 end cell cell space space space space space 2 end cell end table close square brackets plus space open square brackets table row 4 cell space space space 0 end cell row 0 cell space space space 4 end cell end table close square brackets space equals space open square brackets table row cell negative 2 plus 4 end cell cell space space space space space space space space space 1 plus 0 end cell row cell negative 3 plus 0 end cell cell space space space space space minus 2 plus 4 end cell end table close square brackets rightwards double arrow space space space space space space 7 straight A to the power of negative 1 end exponent space equals space open square brackets table row cell space space 2 end cell cell space space space space 1 end cell row cell negative 3 end cell cell space space space 2 end cell end table close square brackets 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 space rightwards double arrow space space space space straight A to the power of negative 1 end exponent space equals space 1 over 7 space open square brackets table row 2 cell space space space space 1 end cell row cell negative 3 end cell cell space space space space space 2 end cell end table close square brackets

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Determinants

For the matrix $straight A space equals space open square brackets table row 2 cell space space space minus 1 end cell row 3 cell space space space space space space 2 end cell end table close square brackets comma$ show that A² – 4 A + 7 I = O. Hence obtain A^–1.

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

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Determinants

For the matrix show that A2 – 4 A + 7 I = O. Hence obtain A–1.

Some More Questions From Determinants Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

For the matrix $straight A space equals space open square brackets table row 2 cell space space space minus 1 end cell row 3 cell space space space space space space 2 end cell end table close square brackets comma$ show that A² – 4 A + 7 I = O. Hence obtain A^–1.