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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 $straight A squared space equals space 1.$

109 Views

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.

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

82 Views

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.

90 Views

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)

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.

straight A equals open square brackets table row 0 cell space space 6 space end cell cell space 7 end cell row cell negative 6 end cell cell 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 1 end cell cell space 1 end cell row 1 cell space 0 end cell cell space space 2 end cell row 1 cell 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 2 end cell row cell negative 2 end cell row cell space space space 3 end cell end table close square brackets straight A plus straight B equals open square brackets table row 0 cell space space 6 space end cell cell space 7 end cell row cell negative 6 end cell cell 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 open square brackets table row 0 cell space 1 end cell cell space 1 end cell row 1 cell space 0 end cell cell space space 2 end cell row 1 cell space 2 end cell cell space 0 end cell end table close square brackets space equals open square brackets table row 0 cell space space 7 end cell cell space 8 end cell row cell negative 5 end cell cell space space 0 end cell cell space 10 end cell row 8 cell negative 6 end cell cell space 0 end cell end table close square brackets therefore space left parenthesis straight A plus straight B right parenthesis straight C space equals space open square brackets table row 0 cell space space 7 end cell cell space 8 end cell row cell negative 5 end cell cell space space 0 end cell cell space 10 end cell row 8 cell negative 6 end cell cell space 0 end cell end table close square brackets space open square brackets table row cell space space space space 2 end cell row cell negative 2 end cell row cell space space space space 3 end cell end table close square brackets space equals space open square brackets table row cell 0 minus 14 plus 24 end cell row cell negative 10 plus 0 plus 30 end cell row cell 16 plus 12 plus 0 end cell end table close square brackets space equals open square brackets table row 10 row 20 row 28 end table close square brackets Again space space space space space space space AC equals open square brackets table row 0 cell space space 6 space end cell cell space 7 end cell row cell negative 6 end cell cell 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 open square brackets table row cell 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 space equals space open square brackets table row cell 0 minus 41 plus 21 end cell row cell negative 10 plus 0 plus 30 end cell row cell 16 plus 012 plus 0 end cell end table close square brackets space equals open square brackets table row 9 row 12 row 30 end table close square brackets AND space space space space space space space BC equals space open square brackets table row 0 cell space 1 end cell cell space 1 end cell row 1 cell space 0 end cell cell space 2 end cell row 1 cell space 2 end cell cell space 0 end cell end table close square brackets space open square brackets table row 2 row cell negative 2 end cell row 3 end table close square brackets space equals space open square brackets table row cell 0 space minus 2 space plus 3 end cell row cell 2 space plus 0 space plus 6 end cell row cell 2 space minus 4 space plus 0 end cell end table close square brackets space equals open square brackets table row cell space space 1 end cell row cell space space 8 end cell row cell negative 2 end cell end table close square brackets therefore space space space space space space AC plus BC equals open square brackets table row 9 row 12 row 30 end table close square brackets space plus open square brackets table row 1 row 8 row cell negative 2 end cell end table close square brackets space equals space open square brackets table row cell 9 plus 1 end cell row cell 12 plus 8 end cell row cell 30 minus 2 end cell end table close square brackets space equals open square brackets table row 10 row 20 row 28 end table close square brackets therefore space space space space space space left parenthesis straight A plus straight B right parenthesis straight C equals AC plus 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 $left parenthesis straight A plus straight B right parenthesis squared equals straight A squared plus 2 AB plus straight B squared$