Which one of the following does NOT equal [| *20c 1xx^2 1yy^2 1zz^2 |?]

[| *20c 1x( x + 1 )x + 1 1y( y + 1 )y + 1 1z( z + 1 )z + 1 |]

This question belongs to Engineering Maths Linear Algebra

Linear Algebra

Which one of the following does NOT equal \[\left| {\begin{array}{*{20}{c}} 1&{\text{x}}&{{{\text{x}}^2}} \\ 1&{\text{y}}&{{{\text{y}}^2}} \\ 1&{\text{z}}&{{{\text{z}}^2}} \end{array}} \right|?\]

A) \[\left| {\begin{array}{*{20}{c}} 1&{{\text{x}}\left( {{\text{x}} + 1} \right)}&{{\text{x}} + 1} \\ 1&{{\text{y}}\left( {{\text{y}} + 1} \right)}&{{\text{y}} + 1} \\ 1&{{\text{z}}\left( {{\text{z}} + 1} \right)}&{{\text{z}} + 1} \end{array}} \right|\] B) \[\left| {\begin{array}{*{20}{c}} 1&{{\text{x}} + 1}&{{{\text{x}}^2} + 1} \\ 1&{{\text{y}} + 1}&{{{\text{y}}^2} + 1} \\ 1&{{\text{z}} + 1}&{{{\text{z}}^2} + 1} \end{array}} \right|\] C) \[\left| {\begin{array}{*{20}{c}} 0&{{\text{x}} - {\text{y}}}&{{{\text{x}}^2} - {{\text{y}}^2}} \\ 0&{{\text{y}} - {\text{z}}}&{{{\text{y}}^2} - {{\text{z}}^2}} \\ 1&{\text{z}}&{{{\text{z}}^2}} \end{array}} \right|\] D) \[\left| {\begin{array}{*{20}{c}} 2&{{\text{x}} + {\text{y}}}&{{{\text{x}}^2} + {{\text{y}}^2}} \\ 2&{{\text{y}} + {\text{z}}}&{{{\text{y}}^2} + {{\text{z}}^2}} \\ 1&{\text{z}}&{{{\text{z}}^2}} \end{array}} \right|\]

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Correct Answer: Option A

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Which one of the following does NOT equal \[\left| {\begin{array}{*{20}{c}} 1&{\text{x}}&{{{\text{x}}^2}} \\ 1&{\text{y}}&{{{\text{y}}^2}} \\ 1&{\text{z}}&{{{\text{z}}^2}} \end{array}} \right|?\]

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