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101.

If space straight A equals open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space 1 end cell end table close square brackets space comma space straight B equals space open square brackets table row 1 cell space space 3 end cell row 2 cell space 1 end cell end table close square brackets

verify that (A + B) (A – B) ≠ A² – B².

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102.

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

find A². Hence find the matrix A⁶.

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103.

IF space matrix space straight A equals open square brackets table row 0 cell space 0 end cell row 4 cell space 0 end cell end table close square brackets

,find A¹⁶

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104.

if space open square brackets table row 1 0 row 0 1 end table close square brackets comma space straight A equals open square brackets table row 0 1 row 0 0 end table close square brackets comma space then space show space that left parenthesis straight a space straight I space plus straight b space straight A right parenthesis cubed equals straight a cubed straight I plus 3 space straight a squared space bA.

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105. Solve for x and y, given that

open square brackets table row 3 cell space space minus 4 end cell row 1 cell space space space space space 2 end cell end table close square brackets space open square brackets table row x row y end table close square brackets equals open square brackets table row cell space 3 end cell row 11 end table close square brackets

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106. Solve for.x and y, given that

open square brackets table row x y row cell 3 y end cell x end table close square brackets open square brackets table row 1 row 2 end table close square brackets equals open square brackets table row 3 row 5 end table close square brackets

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107. $Solve space for space straight x space andy comma space given space that open square brackets table row 2 cell negative 3 end cell row 1 1 end table close square brackets space open square brackets table row straight x row straight y end table close square brackets equals open square brackets table row 1 row 3 end table close square brackets$

open square brackets table row 2 cell negative 3 end cell row 1 1 end table close square brackets space open square brackets table row straight x row straight y end table close square brackets equals open square brackets table row 1 row 3 end table close square brackets rightwards double arrow open square brackets table row cell 2 straight x space minus space 3 straight y end cell row cell straight x plus space space straight y end cell end table close square brackets equals open square brackets table row 1 row 3 end table close square brackets By space definition space of space equality space of space matrices comma space space 2 straight x space – space 3 space straight y space equals space 1 space space space space... left parenthesis 1 right parenthesis space space straight x space plus space straight y space equals space 3 space space space space... left parenthesis 2 right parenthesis space space Multiplying space left parenthesis 1 right parenthesis space by space 1 space and space left parenthesis 2 right parenthesis space by space 3 comma space we space get comma space space 2 space space space space. straight x space – space 3 space straight y space equals space 1 space space 3 space space space space. straight x space plus space 3 space straight y space equals space 9 space space Adding comma space 5 straight x space equals space 10 space rightwards double arrow space straight x space equals space 2 space space therefore space from space left parenthesis 2 right parenthesis comma space 2 space plus straight y space equals space 3 space rightwards double arrow space straight y space equals space 1 space. space space therefore space we space have space straight x space equals space 2 comma space straight y space equals space 1.

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108.

Find space the space values space of space straight a space and space straight b space for space which space the space following space holds space colon open square brackets table row straight a straight b row cell negative straight a end cell cell 2 straight b end cell end table close square brackets space open square brackets table row 2 row cell negative 1 end cell end table close square brackets equals open square brackets table row 5 row 4 end table close square brackets

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109.

Find space the space values space of space straight a space and space straight b space for space which space the space following space holds space colon open square brackets table row 4 2 row 3 cell negative 1 end cell end table close square brackets space open square brackets table row straight a row straight b end table close square brackets equals space open square brackets table row cell negative 4 end cell row 2 end table close square brackets

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110.

Let space straight A equals open square brackets table row 2 cell negative 1 end cell row 3 4 end table close square brackets straight B equals space open square brackets table row 5 2 row 7 4 end table close square brackets comma space straight C equals space open square brackets table row 2 5 row 3 8 end table close square brackets space Find space straight a space matrix space straight D space such space that space CD minus AB equals 0

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