Choose the correct answer in questions 17 to 19: If x, y, z are nonzero real numbers then the inverse of metrix `A=[{:(x,0,0),(0,y,0),(0,0,z):}]`is : (a) `[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}]` (b) `xyz[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}]` ( c) `1/(xyz)[{:(x,0,0),(0,y,0),(0,0,z):}]` (d) `1/(xyz)[{:(1,0,0),(0,1,0),(0,0,1):}]`

Choose the correct answer in questions 17 to 19: If x, y, z are nonzer

1.	Choose the correct answer in questions 17 to 19: If x, y, z are nonzero real numbers then the inverse of metrix `A=[{:(x,0,0),(0,y,0),(0,0,z):}]`is : (a) `[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}]` (b) `xyz[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}]` ( c) `1/(xyz)[{:(x,0,0),(0,y,0),(0,0,z):}]` (d) `1/(xyz)[{:(1,0,0),(0,1,0),(0,0,1):}]`
Answer» Correct Answer - (a) `:." "A=[{:(x,0,0),(0,y,0),(0,0,z):}]` `rArr" "\|A\|=[{:(x,0,0),(0,y,0),(0,0,z):}]=xyzne0` `A_(11)=yz, A_(12)=0, A_(13)=0` `A_(21)=0, A_(22)=zx, A_(23)=0` `A_(31)=0, A_(32)=0, A_(32)=0, A_(33)=xy` `:." adj A"=[{:(yz,0,0),(0,zx,0),(0,0,xy):}]=[{:(yz,0,0),(0,zx,0),(0,0,xy):}]` `"and A"^(-1)=1/\|A\|".adj A"=1/(xyz)[{:(yz,0,0),(0,zx,0),(0,0,xy):}]` `=[{:(1/x,0,0),(0,1/y,0),(0,0,1/z):}]` `=[{:(x^(-1),0,0),(0,y^(-1),0),(0,0,z^(-1)):}]`