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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 $straight A space equals space open square brackets table row 2 cell space space space 1 end cell cell space space space space space 5 end cell row 3 cell space minus 2 end cell cell space space space minus 4 end cell row cell negative 3 end cell cell space 1 end cell cell space space minus 2 end cell end table close square brackets$

74 Views

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.

69 Views

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
$straight A space equals space open square brackets table row 1 cell space space 2 end cell cell space space 3 end cell row 2 cell space space 3 end cell cell space space 2 end cell row 3 cell space 3 end cell cell space space 4 end cell end table close square brackets$

98 Views

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.

74 Views

Short Answer Type

168.

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

71 Views

169.
Find the inverse of $open square brackets table row cell negative 1 end cell cell space space space space 5 end cell row cell negative 3 end cell cell space space space space 2 end cell end table close square brackets$

Let A = $open square brackets table row cell negative 1 end cell cell space space space 5 end cell row cell negative 3 end cell cell space space space 2 end cell end table close square brackets$
$therefore space space open vertical bar straight A close vertical bar space space equals open square brackets table row cell negative 1 end cell cell space space space space 5 end cell row cell negative 3 end cell cell space space space 2 end cell end table close square brackets space equals space minus 2 plus 15 space equals space 13 space not equal to space 0 therefore space space space space space straight A to the power of negative 1 end exponent space exits. space space space space space space space space space straight A subscript 11 space equals space 2 comma space space space straight A subscript 12 space equals space 3 comma space space space straight A subscript 21 space equals space minus 5 comma space space straight A subscript 22 space equals space minus 1 adj space. straight A space equals space open square brackets table row cell straight A subscript 11 end cell cell straight A subscript 12 end cell row cell straight A subscript 21 end cell cell straight A subscript 22 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell space 2 end cell cell space space space 3 end cell row cell negative 5 end cell cell space space minus 1 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row 2 cell space minus 5 end cell row 3 cell negative 1 end cell end table close square brackets straight A to the power of negative 1 end exponent space equals space fraction numerator adj. space straight A over denominator open vertical bar straight A close vertical bar end fraction space equals space 1 over 13 open square brackets table row 2 cell space minus 5 end cell row 3 cell negative 1 end cell end table close square brackets.$