Find a 2 X 2 matrix B such that from Mathematics Matrices
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    Matrices

    Multiple Choice QuestionsShort 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 thatopen 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

    Let space straight B equals space open square brackets table row straight x straight y row straight z straight t end table close square brackets therefore space space space open square brackets table row 2 5 row cell negative 3 end cell 7 end table close square brackets space straight B equals space minus open square brackets table row 2 5 row cell negative 3 end cell 7 end table close square brackets space space open square brackets table row straight X straight y row straight Z straight t end table close square brackets equals open square brackets table row 17 cell negative 1 end cell row 47 cell negative 13 end cell end table close square brackets rightwards double arrow open square brackets table row cell 2 straight x plus 5 straight z end cell cell 2 straight y plus 5 straight t end cell row cell negative 3 straight x plus 7 straight z end cell cell negative 3 straight y plus 7 straight t end cell end table close square brackets equals space open square brackets table row 17 cell negative 1 end cell row 47 13 end table close square brackets
    By definition of equality of matrices, we get
    2x + 5 z = 17    ...(1)
    –3 x + 7 z =47    ...(2)
    2y + 5 t =–1    ...(3)
    –3y + 7 t = – 13    ...(4)
    Multiplying (1) by 3 and (2) by 2, we get,
    6 x + 15z = 51    ...(5)
    –6x + 14 z = 94    ...(6)
    Adding (5) and (6), we get,
    29 z = 145 or z = 5
    ∴ from (1 )2 x + 25 = 17 or 2.x = – 8 ⇒ x = – 4
    Multiplying (3) by 3 and (4) by 2, we get,
    6.y + 15t =.– 3    ...(7)
    – 6 y+ 14 t = – 26    ...(8)
    Adding (7) and (8), we get,
    29 t = – 29 or t = –1
    ∴ from (3) 2y – 5 = – 1 or 2 y = 4 ⇒ y = 2
    we have
    x = – 4, y = 2, z = 5, t = – 1
    therefore space straight B equals space open square brackets table row cell negative 4 end cell 2 row 5 cell negative 1 end cell end table close square brackets
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    113. Without using'the concept of inverse of a matrix, find the matrixopen 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
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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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