Pertanyaan

Diberikan matriks A = ( 1 2 3 8 ) , C = ( 4 1 6 3 ) . Jika A B = C dan B − 1 invers dari B , determinan matriks adalah ....

Diberikan matriks $A = (1238), C = (4163)$ . Jika $A B = C$ dan $B^{- 1}$ invers dari $B$ , determinan matriks B to the power of negative 1 end exponent adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

determinan matriks adalah .

determinan matriks B to the power of negative 1 end exponent

adalah

Pembahasan

ingat: Sifat-sifat determinan: Dengan menggunakan sifat determinan: Jadi, determinan matriks adalah .

ingat: A equals open parentheses table row a b row c d end table close parentheses rightwards arrow open vertical bar A close vertical bar equals a d minus b c

Sifat-sifat determinan:

$ring operator open vertical bar A to the power of T close vertical bar equals open vertical bar A close vertical bar ring operator open vertical bar A to the power of negative 1 end exponent close vertical bar equals fraction numerator 1 over denominator open vertical bar A close vertical bar end fraction ring operator open vertical bar A B close vertical bar equals open vertical bar A close vertical bar times open vertical bar B close vertical bar ring operator open vertical bar k A subscript left parenthesis n cross times n right parenthesis end subscript close vertical bar equals k to the power of n times open vertical bar A close vertical bar$

Dengan menggunakan sifat determinan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals C row cell open vertical bar A B close vertical bar end cell equals cell open vertical bar C close vertical bar end cell row cell open vertical bar A close vertical bar times open vertical bar B close vertical bar end cell equals cell open vertical bar C close vertical bar end cell row cell fraction numerator open vertical bar A close vertical bar over denominator open vertical bar C close vertical bar end fraction end cell equals cell fraction numerator 1 over denominator open vertical bar B close vertical bar end fraction end cell row cell open vertical bar B to the power of negative 1 end exponent close vertical bar end cell equals cell fraction numerator open vertical bar A close vertical bar over denominator open vertical bar C close vertical bar end fraction end cell row blank equals cell fraction numerator 1 times 8 minus 3 times 2 over denominator 4 times 3 minus 6 times 1 end fraction end cell row blank equals cell fraction numerator 8 minus 6 over denominator 12 minus 6 end fraction end cell row blank equals cell 2 over 6 end cell row blank equals cell 1 third end cell end table$

Jadi, determinan matriks B to the power of negative 1 end exponent adalah 1 third .