If   show that A4 = I. Hence find A–1 from Mathematics De

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 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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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.

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 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 ?

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 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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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


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

Now straight A squared space equals space open square brackets table row 3 cell space space minus 3 end cell cell space space 4 end cell row 2 cell space space minus 3 end cell cell space space 4 end cell row 0 cell negative 1 end cell cell space space 1 end cell end table close square brackets space open square brackets table row 3 cell space space space minus 3 end cell cell space space space 4 end cell row 2 cell space space space minus 3 end cell cell space space space 4 end cell row 0 cell space minus 1 end cell cell space space space 1 end cell end table close square brackets space space space space space space space
          equals space open square brackets table row cell 9 minus 6 plus 0 end cell cell space space minus 9 plus 9 minus 4 end cell cell space space 12 minus 12 plus 4 end cell row cell 6 minus 6 plus 0 end cell cell space minus 6 plus 9 minus 4 end cell cell 8 minus 12 plus 4 end cell row cell 0 minus 2 plus 0 end cell cell 0 plus 3 minus 1 end cell cell 0 minus 4 plus 1 end cell end table close square brackets space equals space open square brackets table row 3 cell space space minus 4 end cell cell space space space space 4 end cell row 0 cell space minus 1 end cell cell space space space 0 end cell row cell negative 2 end cell cell space 2 end cell cell space minus 3 end cell end table close square brackets
straight A cubed space equals space open square brackets table row 3 cell space space minus 4 end cell cell space space space space space space 4 end cell row 0 cell space space minus 1 end cell cell space space space space space 0 end cell row cell negative 2 end cell cell space space 2 end cell cell space space minus 3 end cell end table close square brackets space space open square brackets table row 3 cell space minus 3 end cell cell space space 4 end cell row 2 cell negative 3 end cell cell space space 4 end cell row 0 cell negative 1 end cell cell space space 1 end cell end table close square brackets
space space space space space space space equals space open square brackets table row cell 9 minus 8 plus 0 end cell cell space space space minus 9 plus 12 minus 4 end cell cell space space 12 minus 6 plus 4 end cell row cell 0 minus 2 plus 0 end cell cell 0 plus 3 plus 0 end cell cell 0 minus 4 plus 0 end cell row cell negative 6 plus 4 plus 0 end cell cell 6 minus 6 plus 3 end cell cell negative 8 plus 8 minus 3 end cell end table close square brackets space equals space open square brackets table row cell space space 1 end cell cell space space minus 1 end cell cell space space space space 0 end cell row cell negative 2 end cell cell space space space space space 3 end cell cell space minus 4 end cell row cell negative 2 end cell cell space space space space 3 end cell cell space minus 3 end cell end table close square brackets space space space space space space space space space space... left parenthesis 2 right parenthesis
straight A to the power of 4 space equals space open square brackets table row 1 cell space space minus 1 end cell cell space space space space 0 end cell row cell negative 2 end cell cell space space space 3 end cell cell negative 4 end cell row cell negative 2 end cell cell space space 3 end cell cell negative 3 end cell end table close square brackets space space 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 space minus 1 end cell cell space space 1 end cell end table close square brackets
space space space space space space equals space open square brackets table row cell 3 minus 2 plus 0 end cell cell space space space minus 3 plus 3 plus 0 end cell cell space space space space 4 plus 4 plus 0 end cell row cell negative 6 plus 6 plus 0 end cell cell 6 minus 9 plus 4 end cell cell negative 8 plus 12 minus 4 end cell row cell negative 6 plus 6 plus 0 end cell cell 6 minus 9 plus 3 end cell cell negative 8 plus 12 minus 3 end cell end table close square brackets space equals space open square brackets table row 1 cell space space 0 end cell cell space space 0 end cell row 0 cell space 1 end cell cell space space 0 end cell row 0 cell space space 0 end cell cell space space 1 end cell end table close square brackets
therefore space space space space space straight A to the power of 4 space equals space space straight I space space space space rightwards double arrow space space space space straight A to the power of 4 straight A to the power of negative 1 end exponent space space equals IA to the power of negative 1 end exponent space space space space rightwards double arrow space space space space space straight A cubed space equals space straight A to the power of negative 1 end exponent space
rightwards double arrow space space space space space space straight A to the power of negative 1 end exponent space space equals space open square brackets table row 1 cell space space space minus 1 end cell cell space space space space space space 0 end cell row cell negative 2 end cell cell space space space space space 3 end cell cell space space minus 4 end cell row cell negative 2 end cell cell space space space space 3 end cell cell space space minus 3 end cell end table close square brackets space space
              

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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.

74 Views

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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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.

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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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