, find K such that from Mathematics Matrices

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Matrices

Short Answer Type

111.

If space straight A equals space open square brackets table row 3 cell negative 4 end cell row cell negative 1 end cell cell space space space space 2 end cell end table close square brackets space find space straight a space matrix space straight B space such space that space AB space equals space straight I.

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112. Find a 2 X 2 matrix B such that

open square brackets table row 2 5 row cell negative 3 end cell 7 end table close square brackets space space straight B equals open square brackets table row 17 cell negative 1 end cell row 47 cell negative 13 end cell end table close square brackets

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113. Without using'the concept of inverse of a matrix, find the matrix

open square brackets table row straight x straight y row straight z straight u end table close square brackets

such that

open square brackets table row 5 cell negative 7 end cell row cell negative 2 end cell 3 end table close square brackets space open square brackets table row x y row z u end table close square brackets equals space open square brackets table row cell negative 16 end cell cell negative 6 end cell row 7 2 end table close square brackets

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114.

Find space the space matrix space x space so space that space x space space open square brackets table row 1 2 3 row 4 5 6 end table close square brackets equals space open square brackets table row cell negative 7 end cell cell negative 8 end cell cell negative 9 end cell row 2 4 6 end table close square brackets

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115. $If space straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets$ , find K such that $straight A squared minus 8 straight A space plus space straight K space straight I space equals 0$

straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets straight A to the power of 2 space equals end exponent open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets equals open square brackets table row cell 1 plus 0 end cell cell 0 plus 0 end cell row cell negative 1 minus 7 end cell cell 0 plus 49 end cell end table close square brackets equals open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets Now space straight A squared minus 8 straight A plus straight K space straight I space equals 0 rightwards double arrow space space open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets plus open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets plus straight k open square brackets table row 1 0 row 0 1 end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets rightwards double arrow open square brackets table row 1 0 row cell negative 8 end cell 49 end table close square brackets plus open square brackets table row cell negative 8 end cell 0 row 8 cell negative 56 end cell end table close square brackets plus open square brackets table row straight k 0 row 0 straight k end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets rightwards double arrow open square brackets table row cell 1 minus 8 plus straight k end cell cell 0 plus 0 plus 0 end cell row cell negative 8 plus 8 plus 0 end cell cell 49 minus 56 plus straight k end cell end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets rightwards double arrow space straight k minus 7 equals 0 space space space space space space rightwards double arrow straight k equals 7.

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116.

If space straight A equals open square brackets table row 1 0 row cell negative 1 end cell 7 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 comma

2 = 8 A + k I.

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117.

If space straight A equals open square brackets table row 3 cell negative 2 end cell row 4 cell negative 2 end cell end table close square brackets comma

find k so that A² = k A - 2 1

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118.

Solve open parentheses 2 space space 3 close parentheses space space space space open parentheses table row 1 2 row cell negative 3 end cell 0 end table close parentheses open parentheses table row straight x row 3 end table close parentheses equals 0

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119.

If space open square brackets 2 straight x space space space space 3 close square brackets space open square brackets table row 1 2 row cell negative 3 end cell 0 end table close square brackets space open square brackets table row straight x row 3 end table close square brackets equals 0 space comma space find space straight x.

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120.

Find space straight y space if space open square brackets table row straight x 1 end table close square brackets space space open square brackets table row 1 0 row cell negative 2 end cell 3 end table close square brackets space space open square brackets table row straight x row 3 end table close square brackets equals 0

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