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Diketahui matriks A = . Jika |A| menyatakan determ...

Diketahui matriks A = begin mathsize 12px style open parentheses table row cell 1 half end cell cell negative 1 half end cell row cell negative 1 half end cell x end table close parentheses end style. Jika |A| menyatakan determinan A maka geometrI begin mathsize 12px style open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus midline horizontal ellipsis end style konvergen ke...

  1. begin mathsize 12px style fraction numerator 2 x minus 1 over denominator 2 x minus 5 end fraction space d e n g a n space minus 3 over 2 less than x less than 5 over 2 end style

  2. size 12px minus fraction numerator size 12px 2 size 12px x size 12px minus size 12px 1 over denominator size 12px 2 size 12px x size 12px minus size 12px 5 end fraction size 12px space size 12px d size 12px e size 12px n size 12px g size 12px a size 12px n size 12px space size 12px minus size 12px 3 over size 12px 2 size 12px less than size 12px x size 12px less than size 12px 5 over size 12px 2

  3. fraction numerator size 12px 2 size 12px x size 12px minus size 12px 1 over denominator size 12px 2 size 12px x size 12px minus size 12px 5 end fraction size 12px space size 12px d size 12px e size 12px n size 12px g size 12px a size 12px n size 12px space size 12px minus size 12px 3 over size 12px 2 size 12px less than size 12px x size 12px less than size 12px 3 over size 12px 2

  4. begin mathsize 12px style negative fraction numerator 2 x minus 1 over denominator 2 x minus 5 end fraction space d e n g a n space minus 5 over 2 less than x less than 5 over 2 end style

  5. begin mathsize 12px style fraction numerator 2 x minus 1 over denominator 2 x minus 5 end fraction space d e n g a n space 3 over 2 less than x less than 5 over 2 end style

Jawaban:

Menentukan determinan matriks dan deret geometri tak hingga

begin mathsize 12px style A equals open parentheses table row a b row c d end table close parentheses  A equals open parentheses table row cell 1 half end cell cell negative 1 half end cell row cell negative 1 half end cell x end table close parentheses    d e t space A equals open vertical bar A close vertical bar  d e t space A equals a d minus b c  d e t space A equals 1 half x minus open parentheses negative 1 half close parentheses open parentheses negative 1 half close parentheses  d e t space A equals 1 half x minus 1 fourth end style

Rumus deret geometri tak hingga begin mathsize 12px style S subscript infinity equals fraction numerator a over denominator 1 minus r end fraction end style dengan - 1 < r < 1

r = rasio

a = suku pertama

Deret begin mathsize 12px style open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus midline horizontal ellipsis end style memiliki:

a = |A|

r = begin mathsize 12px style U subscript 2 over U subscript 1 equals fraction numerator begin display style open vertical bar A close vertical bar squared end style over denominator open vertical bar A close vertical bar end fraction equals open vertical bar A close vertical bar end style

 

Menentukan deret geometrinya

begin mathsize 12px style open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals S subscript infinity  open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals fraction numerator a over denominator 1 minus r end fraction  open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals fraction numerator open vertical bar A close vertical bar over denominator 1 minus open vertical bar A close vertical bar end fraction  open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals fraction numerator begin display style 1 half end style x minus begin display style 1 fourth end style over denominator 1 minus open parentheses begin display style 1 half end style x minus begin display style 1 fourth end style close parentheses end fraction space open parentheses p e m b i l a n g space d a n space p e n y e b u t space d i k a l i space 4 close parentheses  open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals fraction numerator 2 x minus 1 over denominator 4 minus open parentheses 2 x plus 1 close parentheses end fraction  open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals fraction numerator 2 x minus 1 over denominator 5 minus 2 x end fraction  open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus horizontal ellipsis equals negative fraction numerator 2 x minus 1 over denominator 2 x minus 5 end fraction end style

Diperoleh deret geometrinya size 12px minus fraction numerator size 12px 2 size 12px x size 12px minus size 12px 1 over denominator size 12px 2 size 12px x size 12px minus size 12px 5 end fraction

 

Menentukan batas pada deret geometrinya

begin mathsize 12px style negative 1 less than r less than 1  minus 1 less than open vertical bar A close vertical bar less than 1  minus 1 less than 1 half x minus 1 fourth less than 1 space open parentheses s e m u a space r u a s space d i k a l i space 4 close parentheses  minus 4 less than 2 x minus 1 less than 4 space left parenthesis s e m u a space r u a s space d i t a m b a h space 1 right parenthesis  minus 3 less than 2 x less than 5 space open parentheses s e m u a space r u a s space d i b a g i space 2 close parentheses  minus 3 over 2 less than x less than 5 over 2 end style

Jadi, begin mathsize 12px style open vertical bar A close vertical bar plus open vertical bar A close vertical bar squared plus open vertical bar A close vertical bar cubed plus midline horizontal ellipsis end style = begin mathsize 12px style fraction numerator 2 x minus 1 over denominator 5 minus 2 x end fraction end style dan batasnya begin mathsize 12px style negative 3 over 2 less than x less than 5 over 2 end style

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