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Matrices

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

straight A space equals open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 1 end table close square brackets comma space straight B equals 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 1 end table close square brackets AB equals space 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 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 1 end table close square brackets equals open square brackets table row cell left parenthesis 2 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 1 right parenthesis end cell cell space left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 5 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis negative 2 right parenthesis end cell cell space space left parenthesis 2 right parenthesis left parenthesis negative 1 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 3 right parenthesis left parenthesis 1 right parenthesis end cell row cell left parenthesis negative 3 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis 1 right parenthesis space end cell cell left parenthesis negative 3 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 5 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis negative 2 right parenthesis end cell cell space space left parenthesis negative 3 right parenthesis left parenthesis negative 1 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 0 right parenthesis left parenthesis 1 right parenthesis end cell row cell left parenthesis 5 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis end cell cell space left parenthesis 5 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 5 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 2 right parenthesis space end cell cell space space space left parenthesis 5 right parenthesis left parenthesis negative 1 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis 1 right parenthesis end cell end table close square brackets equals open square brackets table row cell negative 6 plus 0 plus 3 end cell cell 4 minus 5 minus 6 end cell cell negative 2 minus 2 plus 3 end cell row cell 9 plus 0 plus 0 end cell cell negative 6 plus 10 plus 0 end cell cell 3 plus 4 plus 0 end cell row cell negative 15 plus 0 minus 1 end cell cell 10 plus 5 plus 2 end cell cell negative 5 plus 2 minus 1 end cell end table close square brackets equals open square brackets table row cell negative 3 end cell cell negative 7 end cell cell negative 1 end cell row 9 4 7 row cell negative 16 end cell 17 cell negative 4 end cell end table close square brackets also space BA equals 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 1 end table close square brackets 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 equals open square brackets table row cell negative 6 minus 6 minus 5 end cell cell 3 plus 4 minus 1 end cell cell negative 9 plus 0 plus 1 end cell row cell 0 minus 15 plus 10 end cell cell 0 plus 10 plus 2 end cell cell 0 plus 0 minus 2 end cell row cell 2 plus 6 plus 5 end cell cell negative 1 minus 4 plus 1 end cell cell 3 minus 0 minus 1 end cell end table close square brackets equals open square brackets table row cell negative 17 end cell 6 cell negative 8 end cell row cell negative 5 end cell 12 cell negative 2 end cell row 13 cell negative 4 end cell 2 end table close square brackets therefore space AB space not equal to space BA

We conclude that multiplication of matrices A and B is not commutative.

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.

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