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Matrices

Short Answer Type

71.

If A = $open square brackets table row 1 0 row 0 cell negative 1 end cell end table close square brackets space and space straight B equals open square brackets table row 0 1 row 1 0 end table close square brackets$ then show that AB ≠ BA.

89 Views

72.
Find AB, if A = $open square brackets table row 0 cell negative 1 end cell row 0 2 end table close square brackets space and space straight B equals space open square brackets table row 3 5 row 0 0 end table close square brackets$

A equals open square brackets table row 0 cell negative 1 end cell row 0 2 end table close square brackets space straight B equals space open square brackets table row 3 5 row 0 0 end table close square brackets therefore space space space AB equals open square brackets table row 0 cell negative 1 end cell row 0 2 end table close square brackets space open square brackets table row 3 5 row 0 0 end table close square brackets equals open square brackets table row cell 0 plus 0 end cell cell 0 plus 0 end cell row cell 0 plus 0 end cell cell 0 plus 0 end cell end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets equals 0

Note : In the case of real numbers a, b if a b = 0 then either a = 0 or b = 0.
But if the product of two matrices is a zero matrix, then it is not necessary that one of the matrices is a zero matrix.

98 Views

73.

If A = $open square brackets table row 4 2 row cell negative 1 end cell 1 end table close square brackets space and space straight I equals open square brackets table row 1 0 row 0 1 end table close square brackets$ show that (A-2I)(A-3I)=O.

81 Views

74.

Compute the indicated products :

(i) $open square brackets table row straight a straight b row cell negative straight b end cell straight a end table close square brackets open square brackets table row a cell negative b end cell row b a end table close square brackets$

80 Views

75.

Compute the indicated products :

$open square brackets table row 1 row 2 row 3 end table close square brackets space open square brackets table row 2 3 4 end table close square brackets$

135 Views

76.

Compute the indicated products :

$open square brackets table row 1 cell negative 2 end cell row 2 3 end table close square brackets open square brackets table row 1 2 3 row 2 3 1 end table close square brackets$

93 Views

77.

Compute the indicated products

92 Views

78.

Compute the indicated products :

$open square brackets table row 2 1 row 3 2 row cell negative 1 end cell 1 end table close square brackets space open square brackets table row 1 0 1 row cell negative 1 end cell 2 1 end table close square brackets$

103 Views

79.

Compute the indicated products :

$open square brackets table row 3 cell negative 1 end cell 3 row cell negative 1 end cell 0 2 end table close square brackets space open square brackets table row 2 cell negative 3 end cell row 1 0 row 3 1 end table close square brackets$