If ([x] ) is the greatest integer less than or equal to (x ) and (|x| ) is the modulus of (x ), then the system of three equations ( aligned & 2 x+3|y|+5[z]=0, x+|y|-2[z]=4, & x+|y|+[z]=1 has aligned )

Step-by-step solution

Given system of three equations ( aligned 2 x+3|y|+5[z] & =0 x+|y|-2[z] & =4 x+|y|+[z] & =1 aligned ) and According to Cramer's rule, (x= ₁ ,|y|= ₂ and [z]= ₃ ) where, ( aligned & = | array ccc 2 & 3 & 5 1 & 1 & -2 1 & 1 & 1 array | & =2(1+2)-3(1+2)+5(1-1)=-3 ₁ & = | array ccc 0 & 3 & 5 4 & 1 & -2 1 & 1 & 1 array | & =0(1+2)-3(4+2)+5(4-1) & =-18+15=-3 ₂ & = | array ccc 2 & 0 & 5 1 & 4 & -2 1 & 1 & 1 array | & =2(4+2)-0(1+2)+5(1-4)=-3 aligned ) and ( ₃= | array lll 2 & 3 & 0 1 & 1 & 4 1 & 1 & 1 array |=2(l-4)-3(l-4)