If verify that A1 – 6A2 + 9A – 4 I = O and hence find A�
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    Determinants

    Multiple Choice QuestionsLong Answer Type

    211.

    Let A = open square brackets table row 4 cell space space space minus 6 end cell cell space space space space 1 end cell row cell negative 1 end cell cell space minus 1 end cell cell space space 1 end cell row cell negative 4 end cell cell space space space 11 end cell cell negative 1 end cell end table close square brackets.
    Show that A is inevitable. Find adj. A and A Also verify that AA–1 = A–1 A = I.

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    Answer
    212.

    Verify AA–1 = A–1 A = I where
    straight A space equals open square brackets table row 0 cell space space space 0 end cell cell space space minus 1 end cell row 3 cell space space space space 4 end cell cell space space space space space 5 end cell row cell negative 2 end cell cell negative 4 end cell cell space space minus 7 end cell end table close square brackets.

    79 Views
    Answer

    Multiple Choice QuestionsShort Answer Type

    213.

    If straight A space equals space open square brackets table row 3 cell space space minus 3 end cell cell space space space 4 end cell row 2 cell space space minus 3 end cell cell space space 4 end cell row 0 cell space minus 1 end cell cell space space 1 end cell end table close square brackets.  then A3 = A–1 What is adj. A ?

    91 Views
    Answer

    Multiple Choice QuestionsLong Answer Type

    214.

    If straight A space equals space open square brackets table row 1 cell space space minus 1 end cell cell space space 1 end cell row 2 cell space minus 1 end cell cell space space 0 end cell row 1 cell space space space space 0 end cell cell space space 0 end cell end table close square brackets comma find A–1 and show that A–1 = A2.

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    Answer
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    215.

    If straight A space equals space open square brackets table row 3 cell space space minus 3 end cell cell space space space 4 end cell row 2 cell space space minus 3 end cell cell space space space 4 end cell row 0 cell space space minus 1 end cell cell space space space 1 end cell end table close square brackets comma  show that A4 = I. Hence find A–1

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    Answer
    216.

    If A = open square brackets table row 2 cell space space 0 end cell cell space space minus 1 end cell row 5 cell space space 1 end cell cell space space space space 0 end cell row 0 cell space space 1 end cell cell space space space space 3 end cell end table close square brackets comma  prove that A–1 = A–2 – 6 A + 111.

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    Answer
    217.

    If straight A space equals space open square brackets table row 1 cell space space 2 end cell cell space space 2 end cell row 2 cell space space 1 end cell cell space space 2 end cell row 2 cell space space 2 end cell cell space space 1 end cell end table close square brackets comma space Find A–1 and hence prove that A2 – 4A – 5 I = O.

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    Answer
    218.

    For the matrix straight A space equals space open square brackets table row 1 cell space space 1 end cell cell space space space space space 1 end cell row 1 cell space space space 2 end cell cell space minus 3 end cell row 2 cell negative 1 end cell cell space space space space 3 end cell end table close square brackets comma show that A3 + 6A2 + 5A + 11 I = 0. Hence, find A–1.

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    219.

    If straight A space equals space open square brackets table row cell space space 2 end cell cell space space space minus 1 end cell cell space space space space space 1 end cell row cell negative 1 end cell cell space space space space space 2 end cell cell space minus 1 end cell row cell space space 1 end cell cell space space minus 1 end cell cell space space space space 2 end cell end table close square brackets comma
    verify that A1 – 6A2 + 9A – 4 I = O and hence find A–1.

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

    straight A squared space equals space open square brackets table row cell space 2 end cell cell space space space space space minus 1 end cell cell space space space space space 1 end cell row cell negative 1 end cell cell space space space space space space space 2 end cell cell space minus 1 end cell row cell space space 1 end cell cell space space space minus 1 end cell cell space space space space 2 end cell end table close square brackets space open square brackets table row cell space 2 end cell cell space space space minus 1 end cell cell space space space space space space 1 end cell row cell negative 1 end cell cell space space space space space space space 2 end cell cell space space minus 1 end cell row cell space 1 end cell cell space space space minus 1 end cell cell space space space space 2 end cell end table close square brackets space space space space space space space equals open square brackets table row cell 4 plus 1 plus 1 end cell cell space minus 2 minus 2 minus 1 end cell cell space space space 2 plus 1 plus 2 end cell row cell negative 2 minus 2 minus 1 end cell cell space space 1 plus 4 plus 1 end cell cell negative 1 minus 2 minus 2 end cell row cell 2 plus 1 plus 2 end cell cell negative 1 minus 2 minus 2 end cell cell 1 plus 1 plus 4 end cell end table close square brackets space equals space open square brackets table row 6 cell space minus 5 end cell cell space space 5 end cell row cell negative 5 end cell cell space space 6 end cell cell negative 5 end cell row 5 cell negative 5 end cell cell space space 6 end cell end table close square brackets space space space straight A cubed space equals space open square brackets table row cell space space 6 end cell cell space space minus 5 end cell cell space space space space space space space 5 end cell row cell negative 5 end cell cell space space space space space 6 end cell cell space space space minus 5 end cell row cell space 5 end cell cell space space minus 5 end cell cell space space space space space space 6 end cell end table close square brackets space space open square brackets table row 2 cell space space space minus 1 end cell cell space space space space space 1 end cell row cell negative 1 end cell cell space space space space space space 2 end cell cell space space space minus 1 end cell row 1 cell space space space minus 1 end cell cell space space space space space 2 end cell end table close square brackets space space space space equals open square brackets table row 6 cell space space space minus 5 end cell cell space space space space space 5 end cell row cell negative 5 end cell cell space space space space space 6 end cell cell space minus 5 end cell row 5 cell space minus 5 end cell cell space space space space 6 end cell end table close square brackets space open square brackets table row cell space 2 end cell cell space space space minus 1 end cell cell space space space space space 1 end cell row cell negative 1 end cell cell space space space space space 2 end cell cell space minus 1 end cell row 1 cell space space minus 1 end cell cell space space space 2 end cell end table close square brackets space space space space equals space open square brackets table row cell 12 plus 5 plus 5 end cell cell space space space minus 6 minus 10 minus 5 end cell cell space space space 6 plus 5 plus 10 end cell row cell negative 10 minus 6 minus 5 end cell cell space space 5 plus 12 plus 5 end cell cell negative 5 minus 6 minus 10 end cell row cell 10 plus 5 plus 6 end cell cell negative 5 minus 10 minus 6 end cell cell 5 plus 5 plus 12 end cell end table close square brackets space equals space open square brackets table row 22 cell space space minus 21 end cell cell space space 21 end cell row cell negative 21 end cell cell space space space 22 end cell cell negative 21 end cell row 21 cell negative 21 end cell cell space space 22 end cell end table close square brackets

    Consider A3 – 6A2 + 9A – 4 I

    equals space open square brackets table row cell space space 22 end cell cell space space space space minus 21 end cell cell space space space 21 end cell row cell negative 21 end cell cell space space space space 22 end cell cell negative 21 end cell row cell space space 21 end cell cell negative 21 end cell cell space space 22 end cell end table close square brackets minus 6 space open square brackets table row cell space space 6 end cell cell space space space minus 5 end cell cell space space 5 end cell row cell negative 5 end cell cell space space space space space space space 6 end cell cell negative 5 end cell row cell space space 5 end cell cell space space space minus 5 end cell cell space space 6 end cell end table close square brackets plus 9 space open square brackets table row 2 cell space space minus 1 end cell 1 row cell negative 1 end cell cell space space space space space 2 end cell cell negative 1 end cell row 1 cell negative 1 end cell 2 end table close square brackets minus 4 open square brackets table row 1 cell space space 0 end cell cell space 0 end cell row 0 cell space 1 end cell cell space 0 end cell row 0 cell space 0 end cell 1 end table close square brackets equals space open square brackets table row 22 cell space space space minus 21 end cell cell space space 21 end cell row cell negative 21 end cell cell space space space 22 end cell cell space minus 21 end cell row 21 cell space space minus 21 end cell cell space space space space 22 end cell end table close square brackets space plus space open square brackets table row cell negative 36 end cell cell space 30 end cell cell space minus 30 end cell row 30 cell negative 36 end cell cell space space space 30 end cell row 30 30 cell space space minus 36 end cell end table close square brackets plus space open square brackets table row 18 cell space minus 9 end cell cell space space space space 9 end cell row cell negative 9 end cell cell space space space 18 end cell cell negative 9 end cell row 9 cell negative 9 end cell 18 end table close square brackets plus open square brackets table row cell negative 4 end cell cell space space 0 end cell cell space space space space 0 end cell row 0 cell space minus 4 end cell cell space space space space 2 end cell row 0 cell space 0 end cell cell space minus 4 end cell end table close square brackets equals space open square brackets table row cell 22 minus 36 plus 18 minus 4 end cell cell space space space space space minus 21 plus 30 minus 9 plus 0 end cell cell space space space space space space 21 minus 30 plus 9 plus 0 end cell row cell negative 21 plus 30 minus 9 plus 0 end cell cell space space space space 22 minus 36 plus 18 minus 4 end cell cell space space space minus 21 plus 30 minus 9 plus 0 end cell row cell 21 minus 30 plus 9 plus 0 end cell cell space space minus 21 plus 30 minus 9 plus 0 end cell cell space space space space 22 minus 36 plus 18 minus 4 end cell end table close square brackets equals space space open square brackets table row 0 cell space 0 end cell cell space space 0 end cell row 0 cell space 0 end cell cell space 0 end cell row 0 cell space 0 end cell cell space 0 end cell end table close square brackets space equals space straight O space space space space space space space space space therefore space space space space space space straight A cubed minus 6 straight A squared plus 9 straight A minus 4 straight I space space equals space straight O space space space space space space space space space space rightwards double arrow space space space space 4 space straight I space equals space straight A cubed space minus space 6 straight A squared space plus space 9 straight A space space space space space space space space space rightwards double arrow space space space 4 space straight A to the power of negative 1 end exponent space equals space straight A squared space minus space 6 straight A plus space 9 space straight I 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 4 straight A to the power of negative 1 end exponent space equals space open square brackets table row cell space space space space 6 end cell cell space space space minus 5 end cell cell space space space space 5 end cell row cell negative 5 end cell cell space space space space space space 6 end cell cell negative 5 end cell row cell space space 5 end cell cell negative 5 end cell cell space space space space 6 end cell end table close square brackets minus 6 space open square brackets table row 2 cell space space minus 1 end cell cell space space 1 end cell row cell negative 1 end cell cell space space space space space 2 end cell cell negative 1 end cell row 1 cell negative 1 end cell 2 end table close square brackets space plus space 9 space open square brackets table row 1 cell space space space space 0 end cell cell space space 0 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 0 cell space 0 end cell cell space 1 end cell end table close square brackets space

               rightwards double arrow space space space 4 straight A to the power of negative 1 end exponent space equals space open square brackets table row cell space space space 6 end cell cell space space minus 5 end cell cell space space space 5 end cell row cell negative 5 end cell cell space space space space space 6 end cell cell negative 5 end cell row cell space space space 5 end cell cell space space minus 5 end cell cell space space space 6 end cell end table close square brackets plus space open square brackets table row cell negative 12 end cell cell space 6 end cell cell space minus 6 end cell row cell space 6 end cell cell negative 12 end cell cell space space space space 6 end cell row cell negative 6 end cell 6 cell negative 12 end cell end table close square brackets plus space open square brackets table row 9 cell space 0 end cell cell space space 0 end cell row 0 cell space 9 end cell cell space 0 end cell row 0 cell space 0 end cell cell space 9 end cell end table close square brackets rightwards double arrow space space space space 4 straight A to the power of negative 1 end exponent space equals space open square brackets table row cell 6 minus 12 plus 9 end cell cell space space space space space minus 5 plus 6 plus 0 end cell cell space space space space space space 5 minus 6 plus 0 end cell row cell negative 5 plus 6 plus 0 end cell cell space space space space 6 minus 12 plus 9 end cell cell space space space space minus 5 plus 6 plus 0 end cell row cell 5 minus 6 plus 0 end cell cell space space minus 5 plus 6 plus 0 end cell cell space space space space space 6 minus 12 plus 9 end cell end table close square brackets rightwards double arrow space space space space space space 4 straight A to the power of negative 1 end exponent space equals space open square brackets table row cell 6 minus 12 plus 9 end cell cell space space space space minus 5 plus 6 plus 0 end cell cell space space space space space space 5 minus 6 plus 0 end cell row cell negative 5 plus 6 plus 0 end cell cell space space space space space 6 minus 12 plus 9 end cell cell space space space minus 5 plus 6 plus 0 end cell row cell 5 minus 6 plus 0 end cell cell space minus 5 plus 6 plus 0 end cell cell space space space space space space 6 minus 12 plus 9 end cell end table close square brackets rightwards double arrow space space space space space space 4 straight A to the power of negative 1 end exponent space equals space open square brackets table row 3 cell space space space space 1 end cell cell space space space minus 1 end cell row 1 cell space space space space 3 end cell cell space space space space 1 end cell row cell negative 1 end cell cell space space space 1 end cell cell space space space 3 end cell end table close square brackets rightwards double arrow space space space space space straight A to the power of negative 1 end exponent space equals space 1 fourth open square brackets table row 3 cell space space space 1 end cell cell space space space minus 1 end cell row 1 cell space space space 3 end cell cell space space space space 1 end cell row cell negative 1 end cell cell space space 1 end cell cell space space space 3 end cell end table close square brackets.
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    220.

    Compute (AB)-1  where straight A space equals space open square brackets table row 5 cell space space space 0 end cell cell space space 4 end cell row 2 cell space space 3 space end cell cell space 2 end cell row 1 cell space 2 end cell cell space 1 end cell end table close square brackets comma space space space straight B to the power of negative 1 end exponent space equals space open square brackets table row 1 cell space space 2 end cell cell space space 3 end cell row 1 cell space space 4 end cell cell space space 3 end cell row 1 cell space space 3 end cell cell space space 4 end cell end table close square brackets

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