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Pertanyaan

Tentukan bayangan dari garis atau kurva berikut oleh transformasi matriks yang diberikan:

begin mathsize 14px style x squared plus y squared equals 25 end style oleh begin mathsize 14px style T equals open square brackets table row 2 cell negative 2 end cell row 7 cell negative 4 end cell end table close square brackets end style

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

bayangan dari garis atau kurva begin mathsize 14px style x squared plus y squared equals 25 end style oleh transformasi matriks begin mathsize 14px style T equals open square brackets table row 2 cell negative 2 end cell row 7 cell negative 4 end cell end table close square brackets end style adalah begin mathsize 14px style x equals square root of fraction numerator 44 x y minus 8 y squared plus 900 over denominator 65 end fraction end root end style.

Pembahasan

begin mathsize 14px style open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets equals open square brackets table row a b row c d end table close square brackets open square brackets table row x row y end table close square brackets open square brackets table row x row y end table close square brackets equals fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end style

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end cell equals cell open square brackets table row 2 cell negative 2 end cell row 7 cell negative 4 end cell end table close square brackets open square brackets table row x row y end table close square brackets end cell row cell open square brackets table row x row y end table close square brackets end cell equals cell open square brackets table row cell negative 4 end cell 2 row cell negative 7 end cell 2 end table close square brackets open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 4 right parenthesis left parenthesis 2 right parenthesis minus left parenthesis 2 right parenthesis left parenthesis negative 7 right parenthesis end fraction open square brackets table row cell negative 4 end cell 2 row cell negative 7 end cell 2 end table close square brackets open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator negative 8 plus 14 end fraction open square brackets table row cell negative 4 end cell 2 row cell negative 7 end cell 2 end table close square brackets open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end cell row blank equals cell 1 over 6 open square brackets table row cell negative 4 end cell 2 row cell negative 7 end cell 2 end table close square brackets open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 over 6 end cell cell 2 over 6 end cell row cell negative 7 over 6 end cell cell 2 over 6 end cell end table close square brackets open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 over 6 x apostrophe plus 2 over 6 y apostrophe end cell row cell negative 7 over 6 x apostrophe plus 2 over 6 y apostrophe end cell end table close square brackets end cell row x equals cell negative 4 over 6 x apostrophe plus 2 over 6 y apostrophe end cell row y equals cell negative 7 over 6 x apostrophe plus 2 over 6 y apostrophe end cell end table end style

Substitusi

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 25 row cell open parentheses negative 4 over 6 x apostrophe plus 2 over 6 y apostrophe close parentheses squared plus open parentheses negative 7 over 6 x apostrophe plus 2 over 6 y apostrophe close parentheses squared end cell equals 25 row cell 65 over 36 x apostrophe squared minus 44 over 36 x apostrophe y apostrophe plus 8 over 36 y apostrophe squared end cell equals 25 row cell 65 x apostrophe squared minus 44 x apostrophe y apostrophe plus 8 y apostrophe squared end cell equals 900 row cell 65 x apostrophe squared end cell equals cell 44 x apostrophe y apostrophe minus 8 y apostrophe squared plus 900 end cell row cell x apostrophe squared end cell equals cell fraction numerator 44 x apostrophe y apostrophe minus 8 y apostrophe squared plus 900 over denominator 65 end fraction end cell row cell x apostrophe end cell equals cell square root of fraction numerator 44 x apostrophe y apostrophe minus 8 y apostrophe squared plus 900 over denominator 65 end fraction end root end cell row x equals cell square root of fraction numerator 44 x y minus 8 y squared plus 900 over denominator 65 end fraction end root end cell end table end style 

Jadi, bayangan dari garis atau kurva begin mathsize 14px style x squared plus y squared equals 25 end style oleh transformasi matriks begin mathsize 14px style T equals open square brackets table row 2 cell negative 2 end cell row 7 cell negative 4 end cell end table close square brackets end style adalah begin mathsize 14px style x equals square root of fraction numerator 44 x y minus 8 y squared plus 900 over denominator 65 end fraction end root end style.

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Tentukan bayangan dari garis atau kurva berikut oleh transformasi matriks yang diberikan: y=x2−2x oleh T=[32​43​]

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