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Compute the adjoint of the matrix $straight A space equals space open square brackets table row 1 cell space space space space space space 2 end cell row 3 cell space space minus 5 end cell end table close square brackets$
and verify that A (Adj A) = | A | 1.

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Long Answer Type

162.

Verify that A (adj A) = (adj A) = | A | I
where $straight A space equals space open square brackets table row 2 cell space space space 1 end cell cell space space space space space 5 end cell row 3 cell space minus 2 end cell cell space space space minus 4 end cell row cell negative 3 end cell cell space 1 end cell cell space space minus 2 end cell end table close square brackets$

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163.

Verify that A (adj A) = (adj A) = | A | I
where

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Short Answer Type

164. Verify A(adj A) = (adj A) A = | A | 1 for
$straight A space equals space open square brackets table row cell space space space 2 end cell cell space space space space 3 end cell row cell negative 4 end cell cell space space minus 6 end cell end table close square brackets.$

Let space straight A space equals space open square brackets table row cell space space space 2 end cell cell space space space space space space 3 end cell row cell negative 4 end cell cell space space minus 6 end cell end table close square brackets straight A subscript 11 space equals negative 6 comma space space straight A subscript 12 space equals space 4 comma space space straight A subscript 21 space equals negative 3 comma space space straight A subscript 22 space equals space 2

therefore space space space space space space space space space space space adj. space straight A space equals space open square brackets table row cell straight A subscript 11 end cell cell space space straight A subscript 12 end cell row cell straight A subscript 21 end cell cell space space straight A subscript 22 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell negative 6 end cell cell space space 4 end cell row cell negative 3 end cell cell space space 2 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell negative 6 end cell cell space space minus 3 end cell row 4 cell space 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 open vertical bar straight A close vertical bar space equals space open vertical bar table row 2 cell space space space space space 3 end cell row cell negative 4 end cell cell space space space minus 6 end cell end table close vertical bar space equals space minus 12 plus 12 space equals space 0 Now space straight A left parenthesis adj space straight A right parenthesis space equals space open square brackets table row 2 cell space space space space space space 3 end cell row cell negative 4 end cell cell space space minus 6 end cell end table close square brackets space open square brackets table row cell negative 6 end cell cell space minus 3 end cell row 4 cell space space space space 2 end cell end table close square brackets space equals space open square brackets table row cell negative 12 plus 12 end cell cell space space space minus 6 plus 6 end cell row cell 24 minus 24 end cell cell space space space space space space space 12 minus 12 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 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 space space equals 0 space open square brackets table row 1 cell space space space 0 end cell row 0 cell space space 1 end cell end table close square brackets space space equals space open vertical bar straight A close vertical bar space straight I space space space space space space space space space space left parenthesis adj space straight A right parenthesis thin space straight A space equals space open square brackets table row cell negative 6 end cell cell space space space space minus 3 end cell row 4 cell 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 space space space space 3 end cell row cell negative 4 end cell cell space space space space space minus 6 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 equals space open square brackets table row cell negative 12 plus 12 end cell cell space space space space space minus 18 plus 18 end cell row cell 8 minus 8 end cell cell space space space space space space 12 minus 12 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 0 cell space space 0 end cell row 0 cell space space 0 end cell end table close square brackets space space equals space 0 open square brackets table row 1 cell space space 0 end cell row 0 cell space space space 1 end cell end table close square brackets space equals space open vertical bar straight A close vertical bar space straight I therefore space space space straight A left parenthesis adj space straight A right parenthesis space equals space left parenthesis adj space straight A right parenthesis thin space straight A space equals space open vertical bar straight A close vertical bar space straight I.

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Long Answer Type

165.

Verify A(adj A) = (adj A) A = | A | 1 for the matrix
$straight A space equals space open square brackets table row 1 cell space space space space 1 end cell cell space space space space space space 2 end cell row 3 cell space space space space 0 end cell cell space space minus 2 end cell row 1 cell space space space space 0 end cell cell space space space space space 3 end cell end table close square brackets.$

73 Views

166.

Verify that A(adj. A) = (adj. A) A = | A | I where
$straight A space equals space open square brackets table row 1 cell space space 2 end cell cell space space 3 end cell row 2 cell space space 3 end cell cell space space 2 end cell row 3 cell space 3 end cell cell space space 4 end cell end table close square brackets$

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167.

If $straight A space equals space open square brackets table row 1 cell space minus 1 end cell cell space space 1 end cell row 2 cell space 3 end cell cell space space 0 end cell row 18 cell space 2 end cell cell space space 10 end cell end table close square brackets comma$
then verify that A (adj. A) = O.

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Short Answer Type

168.

Find the inverse of $open square brackets table row 2 cell space space space minus 2 end cell row 4 cell space space space space space space 3 end cell end table close square brackets$

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169.

Find the inverse of $open square brackets table row cell negative 1 end cell cell space space space space 5 end cell row cell negative 3 end cell cell space space space space 2 end cell end table close square brackets$

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170. Find the sum of

open square brackets table row 2 cell space space space space minus 3 end cell row 5 cell space space space minus 7 end cell end table close square brackets

and its multiplication inverse.

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