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Short Answer Type

91.

If $straight A equals space open square brackets table row 0 0 1 row 0 1 0 row 1 0 0 end table close square brackets comma space$ verify that $straight A squared space equals space 1.$

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Long Answer Type

92.

If $straight A equals open square brackets table row 1 cell space space 2 end cell row 3 cell space space 4 end cell row 5 cell space space 6 end cell end table close square brackets space and space straight B equals open square brackets table row 4 cell space 5 end cell cell space space 6 end cell row 7 cell space 8 end cell cell space space 9 end cell end table close square brackets$ then find AB and BA. Is AB= BA ? What conclusion do you draw?

80 Views

93.

$If space straight A equals open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 cell negative 1 end cell end table close square brackets comma straight B equals space open square brackets table row cell negative 3 end cell 2 cell negative 1 end cell row 0 5 2 row 1 cell negative 2 end cell cell negative 1 end cell end table close square brackets space then find space AB space and space BA. space Is space AB equals BA ? space What space conclusion space do space you space draw$

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Short Answer Type

94.

show that $open square brackets table row 5 cell space minus 1 end cell row 6 cell space space space space 7 end cell end table close square brackets open square brackets table row 2 cell space 1 end cell row 3 cell space 4 end cell end table close square brackets not equal to open square brackets table row 2 cell space 1 end cell row 3 cell space 4 end cell end table close square brackets open square brackets table row cell 5 space space end cell cell negative 1 end cell row 6 cell space space space 7 end cell end table close square brackets$

73 Views

95.

show that $open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets not equal to open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets$

74 Views

96.

If space straight A equals open square brackets table row 1 cell negative 1 end cell 1 row 0 2 1 end table close square brackets comma space straight B space open square brackets table row 1 cell negative 1 end cell 0 row 0 1 cell negative 1 end cell row 1 1 1 end table close square brackets space comma straight C space open square brackets table row 1 0 row 0 1 row 1 1 end table close square brackets space verify space that space straight A space left parenthesis BC right parenthesis equals left parenthesis AB right parenthesis space straight C.

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Long Answer Type

97. $if space straight A equals open square brackets table row 1 1 1 row 2 0 cell negative 3 end cell row 3 cell negative 1 end cell 2 end table close square brackets comma straight B equals open square brackets table row 1 3 row 0 2 row cell negative 1 end cell 4 end table close square brackets comma space and space straight C equals open square brackets table row 1 2 3 cell negative 4 end cell row 2 0 cell negative 2 end cell 1 end table close square brackets$

Find A(BC), (AB)C and show that (AB(BC).)C=A(BC)

straight A equals open square brackets table row 1 1 cell negative 1 end cell row 2 0 3 row 3 cell negative 1 end cell 2 end table close square brackets comma straight B equals open square brackets table row 1 3 row 0 2 row cell negative 1 end cell 4 end table close square brackets comma space a n d space straight C equals open square brackets table row 1 2 3 cell negative 4 end cell row 2 0 cell negative 2 end cell 1 end table close square brackets AB equals open square brackets table row 1 1 cell negative 1 end cell row 2 0 3 row 3 cell negative 1 end cell 2 end table close square brackets space open square brackets table row 1 3 row 0 2 row cell negative 1 end cell 4 end table close square brackets space equals open square brackets table row cell 1 plus 0 plus 1 end cell cell 3 plus 2 minus 4 end cell row cell 2 plus 0 minus 3 end cell cell 6 plus 0 plus 12 end cell row cell 3 plus 0 minus 2 end cell cell 9 minus 2 plus 8 end cell end table close square brackets space equals space open square brackets table row 2 1 row cell negative 1 end cell 18 row 1 15 end table close square brackets space AB left parenthesis straight C right parenthesis equals open square brackets table row 2 1 row cell negative 1 end cell 18 row 1 15 end table close square brackets space open square brackets table row 1 2 3 cell negative 4 end cell row 2 0 cell negative 2 end cell 1 end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row cell 2 plus 2 end cell cell 4 plus 0 end cell cell 6 minus 2 end cell cell negative 8 plus 1 end cell row cell negative 1 plus 36 end cell cell negative 2 plus 0 end cell cell negative 3 minus 36 end cell cell 4 plus 18 end cell row cell 1 plus 30 end cell cell 2 plus 0 end cell cell 3 minus 36 end cell cell negative 4 plus 15 end cell end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row 4 4 4 cell negative 7 end cell row 35 cell negative 2 end cell cell negative 39 end cell 22 row 31 2 cell negative 27 end cell 11 end table close square brackets NOW BC space equals space open square brackets table row 1 3 row 0 2 row cell negative 1 end cell 4 end table close square brackets space open square brackets table row 1 2 3 cell negative 4 end cell row 2 0 cell negative 2 end cell 1 end table close square brackets space space space space space space space space equals open square brackets table row cell 1 plus 6 end cell cell 2 plus 0 end cell cell 3 minus 6 end cell cell negative 4 plus 3 end cell row cell 0 plus 4 end cell cell 0 plus 0 end cell cell 0 minus 4 end cell cell 0 plus 2 end cell row cell negative 1 plus 8 end cell cell negative 2 plus 0 end cell cell negative 3 minus 8 end cell cell 4 plus 4 end cell end table close square brackets space space space space space space space space space equals space open square brackets table row 7 2 cell negative 3 end cell cell negative 1 end cell row 4 0 cell negative 4 end cell 2 row 7 cell negative 2 end cell cell negative 11 end cell 8 end table close square brackets space space

therefore space straight A left parenthesis BC right parenthesis equals open square brackets table row 1 1 cell negative 1 end cell row 2 0 3 row 3 cell negative 1 end cell 2 end table close square brackets space open square brackets table row 7 2 cell negative 3 end cell cell negative 1 end cell row 4 0 cell negative 4 end cell 2 row 7 cell negative 2 end cell cell negative 11 end cell 8 end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row cell 7 plus 4 minus 7 end cell cell 2 plus 0 plus 2 end cell cell negative 3 minus 4 plus 11 end cell cell negative 1 plus 2 minus 8 end cell row cell 14 plus 0 plus 21 end cell cell 4 plus 0 minus 6 end cell cell negative 6 plus 0 minus 33 end cell cell negative 2 plus 0 plus 24 end cell row cell 21 minus 4 plus 14 end cell cell 6 plus 0 minus 4 end cell cell negative 9 plus 4 minus 22 end cell cell negative 3 minus 2 plus 16 end cell end table close square brackets space space space space space space space space space space space space equals space open square brackets table row 4 4 4 cell negative 7 end cell row 35 cell negative 2 end cell cell negative 39 end cell 22 row 31 2 cell negative 27 end cell 11 end table close square brackets space space space space space space space space therefore space left parenthesis AB right parenthesis straight C space equals space straight A left parenthesis BC right parenthesis 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

75 Views

Short Answer Type

98.

If space straight A equals open square brackets table row 0 cell space space 6 end cell cell space 7 end cell row cell negative 6 end cell cell space space space 0 end cell cell space 8 end cell row 7 cell negative 8 end cell cell space 0 end cell end table close square brackets space comma space straight B equals open square brackets table row 0 cell space space 1 end cell cell space space 1 end cell row 1 cell space space 0 end cell cell space 2 end cell row 1 cell space space 2 end cell cell space 0 end cell end table close square brackets space comma space straight C equals open square brackets table row cell space space space space 2 end cell row cell negative 2 end cell row cell space space space 3 end cell end table close square brackets

Calculate AC,BC and (A+B) C. Also, verify that (A+B) C-AC+BC.

75 Views

99.

if space straight A space equals open square brackets table row 1 cell negative 1 end cell row 2 3 end table close square brackets comma space straight B space open square brackets table row 2 cell space 1 end cell row 1 cell space 0 end cell end table close square brackets space comma space verify space that space left parenthesis straight A plus straight B right parenthesis squared space not equal to space straight A squared space plus 2 AB plus straight B squared

82 Views

100.

Give an example of two square matrices of order 2x2 each so that $left parenthesis straight A plus straight B right parenthesis squared equals straight A squared plus 2 AB plus straight B squared$

74 Views

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97. Find A(BC), (AB)C and show that (AB(BC).)C=A(BC)

Short Answer Type