Home
Class 12
MATHS
If x ,\ y ,\ z are non-zero real numbe...

If `x ,\ y ,\ z` are non-zero real numbers, then the inverse of the matrix `A=[(x,0, 0),( 0,y,0),( 0, 0,z)]` , is `[x^(-1)0 0 0y^(-1)0 0 0z^(-1)]` (b) `x y z[x^(-1)0 0 0y^(-1)0 0 0z^(-1)]` (c) `1/(x y z)[x0 0 0y0 0 0z]` (d) `1/(x y z)[1 0 0 0 1 0 0 0 1]`

Text Solution

Verified by Experts

We have given that `A=[(x,0, 0),( 0,y,0),( 0, 0,z)]`
Here, `∣A∣=x(yz−0)+0+0`
`⇒∣A∣=xyz `
Since, x,y,z are non-zero real numbers.
So, `A^(−1)`exists.
`A^(−1)=(adj A)/|A|` and `adjA=C^T`
`C_(11)=(-1)^(1+1)[(y,0),(0,z)]`
`⇒C_(11)=yz`
...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF MATRICES

    RD SHARMA|Exercise Solved Examples And Exercises|410 Videos

Similar Questions

Explore conceptually related problems

The inverse of the matrix [[x, 0, 0], [0, y, 0], [0, 0, z]] is

If x, y, z are non-zero real numbers, then the inverse of matrix 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 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):}]

6.If A=[[x,0,0],[0,y,0],[0,0,z]] then A^(-1) is

If [(1, 0 ,0 ),(0,y,0),( 0, 0, 1)][(x),(-1),(z)]=[(1),( 0),( 1)] , find x ,\ y\ a n d\ z .

If [(1,0,0 ), (0,-1,0), (0,0, -1)][(x),(y),( z)]=[(1),(0),(1)] , find x ,\ y\ a n d\ z .

If [(1 ,0, 0) ,(0 ,1, 0),( 0 ,0 ,1)][(x),( y),( z)]=[(1),(-1),( 0)] , find x ,\ y\ a n d\ z .

The solutiion of (x,y,z) the equation [(-1,0,1),(-1,1,0),(0,-1,1)][(x),(y),(z)]=[(1),(1),(2)] is (x,y,z)

Lines (x-1)/1 = (y-1)/2 = (z-3)/0 and (x-2)/0 = (y-3)/0 = (z-4)/1 are