Question

o determinante da matriz

Answer 1

Resposta:

DetA = 0

Explicação passo a passo:

$A=\left[\begin{array}{ccc}c&x&(3x-2b)\\c&y&(3y-2b)\\c&z&(3z-2b)\end{array}\right]$

$DetA=a_{11} .a_{22} .a_{33} + a_{12} .a_{23} .a_{31} + a_{13} .a_{21} .a_{32} - a_{31} .a_{22} .a_{13} - a_{32} .a_{23} .a_{11} - a_{33} .a_{21} .a_{12}$

$DetA=c .y .(3z-2b) + x .(3y-2b) .c + (3x-2b) .c .z - c .y .(3x-2b) - z .(3y-2b) .c - (3z-2b) .c .x\\\\DetA=cy .(3z-2b) + cx .(3y-2b) + cz .(3x-2b) - cy .(3x-2b) - cz .(3y-2b) - cx .(3z-2b)\\\\DetA=\bold{3cyz}-2bcy + 3cxy-2bcx + 3cxz-2bcz - 3cxy+2bcy \bold{- 3cyz}+2bcz - 3cxz+2bcx\\\\DetA=\bold{-2bcy} + 3cxy-2bcx + 3cxz-2bcz - 3cxy\bold{+2bcy} +2bcz - 3cxz+2bcx\\\\DetA=\bold{3cxy}-2bcx + 3cxz-2bcz \bold{- 3cxy} +2bcz - 3cxz+2bcx\\\\DetA=\bold{-2bcx} + 3cxz-2bcz +2bcz - 3cxz\bold{+2bcx}$

$DetA=\bold{3cxz}-2bcz +2bcz \bold{- 3cxz}\\\\DetA=\bold{-2bcz +2bcz}\\\\\bold{DetA=0}$