Dik: matriks M (1/akar2 1/2

1/2 1/2)

tentukan inversnya.. mohon dijawab yaaaa

Dik: matriks M (1/akar2 1/2

Jawaban Terkonfirmasi

$M^{-1}= frac{1}{det(M)}times adjoin(M)$

$M=left[begin{array}{cc} {a} & {b} \ {c} & {d} end{array}right]$

$M^{-1}= frac{1}{ad-bc}times left[begin{array}{cc}d&-b\-c&aend{array}right]$

$M^{-1}= frac{1}{( frac{1}{ sqrt{2} })( frac{1}{2} )-( frac{1}{2} )( frac{1}{2} )}times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= frac{1}{( frac{1}{ 2sqrt{2} })-( frac{1}{4} )}times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= frac{4 sqrt{2} }{( frac{4 sqrt{2}}{ 2sqrt{2} })-( frac{4 sqrt{2}}{4} )}times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= frac{4 sqrt{2} }{(2)-( sqrt{2} )}times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= frac{4 sqrt{2}(2+sqrt{2} ) }{(2-sqrt{2})(2+sqrt{2} )}times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= frac{8 sqrt{2}+8 }{4-2}times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= (4sqrt{2}+4)times left[begin{array}{cc}( frac{1}{2} )&-( frac{1}{2} )\-( frac{1}{2} )&( frac{1}{ sqrt{2} } )end{array}right]$

$M^{-1}= left[begin{array}{cc} frac{4sqrt{2}+4}{2} &- frac{4sqrt{2}+4}{2} \- frac{4sqrt{2}+4}{2} & frac{4sqrt{2}+4}{ sqrt{2} } end{array}right]$

$M^{-1}= left[begin{array}{cc} 2sqrt{2}+2 &- (2sqrt{2}+2)\- (2sqrt{2}+2) & 4+2 sqrt{2} } end{array}right]$

$M^{-1}= left[begin{array}{cc} 2sqrt{2}+2 &-2sqrt{2}-2\-2sqrt{2}-2 & 4+2 sqrt{2} } end{array}right]$

Jawaban Terkonfirmasi

M = [1/akar2 1/2]
[1/2 1/2]

cari determinan=
(1/akar2 . 1/2) – (1/2 .1/2) = 1/2 akar2 -1/4 = 1/8 – 1/4 = -1/8

adjoin =
[1/2 -1/2]
[-1/2 1/akar2]

invers = 1/determinan . adjoin
         = 1 / -1/8 . [1/2       -1/2]
                       [-1/2     1/akar2]
         = 1 . -8/1 . [1/2    -1/2]
                          [-1/2 1/akar2]
         = -8 . [1/2      -1/2]
                  [-1/2     1/akar2]
   = [-4 4]
[4    -4/akar2]
kalau ada kesalahan mohon maaf