Diketahui matriks dan matriks . Jika , matriks ad...

Diketahui matriks $A equals open parentheses table row 1 6 row 9 cell negative 4 end cell end table close parentheses$ dan matriks $C equals open parentheses table row 17 8 row 46 cell negative 45 end cell end table close parentheses$ . Jika $2 A B minus I equals C$ , matriks $B$ adalah ...

Jawaban:

Ingat operasi hitung pada matriks baik operasi pengurangan dua matriks, penjumlahan dua matriks, perkalian dua matriks, perkalian dengan skalar dan juga invers matriks.

Menentukan persamaan untuk mengetahui matriks $B$ .

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 A B minus I end cell equals C row cell 2 A B end cell equals cell C plus I end cell row cell A to the power of negative 1 end exponent 2 A B end cell equals cell A to the power of negative 1 end exponent left parenthesis C plus I right parenthesis end cell row cell 2 B end cell equals cell A to the power of negative 1 end exponent left parenthesis C plus I right parenthesis end cell row B equals cell 1 half A to the power of negative 1 end exponent left parenthesis C plus I right parenthesis end cell end table$

Karena dibutuhkan invers matriks $A$ , maka harus menentukan invers matriks $A$ terlebih dahulu.

$table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row 1 6 row 9 cell negative 4 end cell end table close parentheses end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator negative 4 minus 54 end fraction open parentheses table row cell negative 4 end cell cell negative 9 end cell row cell negative 6 end cell 1 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 58 end fraction open parentheses table row cell negative 4 end cell cell negative 9 end cell row cell negative 6 end cell 1 end table close parentheses end cell end table$

Menentukan matriks $B$ .

$table attributes columnalign right center left columnspacing 0px end attributes row B equals cell 1 half A to the power of negative 1 end exponent left parenthesis C plus I right parenthesis end cell row blank equals cell 1 half times fraction numerator 1 over denominator negative 58 end fraction open parentheses table row cell negative 4 end cell cell negative 9 end cell row cell negative 6 end cell 1 end table close parentheses open parentheses open parentheses table row 17 8 row 46 cell negative 45 end cell end table close parentheses plus open parentheses table row 1 0 row 0 1 end table close parentheses close parentheses end cell row blank equals cell 1 half times fraction numerator 1 over denominator negative 58 end fraction open parentheses table row cell negative 4 end cell cell negative 9 end cell row cell negative 6 end cell 1 end table close parentheses open parentheses table row 18 8 row 46 cell negative 44 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 58 end fraction open parentheses table row cell negative 4 end cell cell negative 9 end cell row cell negative 6 end cell 1 end table close parentheses open parentheses table row 9 4 row 23 cell negative 22 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 58 end fraction open parentheses table row cell negative 36 minus 138 end cell cell negative 16 plus 132 end cell row cell negative 81 plus 23 end cell cell negative 36 minus 22 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 58 end fraction open parentheses table row cell negative 174 end cell 116 row cell negative 58 end cell cell negative 58 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 cell negative 2 end cell row 1 1 end table close parentheses end cell end table$

Jadi, dapat disimpulkan bahwa matriks $B$ adalah $open parentheses table row 3 cell negative 2 end cell row 1 1 end table close parentheses$ .

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