Home
Class 12
MATHS
show that the matrix A=[(2,-2,-4),(-1,...

show that the matrix
`A=[(2,-2,-4),(-1,3,4),(1,-2,-3)]` is idempotent.

Text Solution

Verified by Experts

`A^(2)=A.A=[(2,-2,-4),(-1,3,4),(1,-2,-3)]xx[(2,-2,-4),(-1,3,4),(1,-2,-3)]`
`=[{:(2.2+(-2).(-1)(-4).1),((-1).2+3.(-1)+4.1),(12+(-2).(-1)+(-3).1),(2.(-2)+(-2).3+(-4).(-2)),((-1).(-2)+3.3+4.(-2)),(1.(-2)+(-2).3+(-3).(-2)),(2.(-4)+(-2).4+(-4).(-3)),((-1).(-4)+3.4.+4.(-3)),(1.(-4)+(-2).4+(-3).(-3)):}`
`[(2,-2,-4),(-1,3,4),(1,-2,-3)]=A`
Hence the matrix A is idempotent.
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that the matrix [{:( 1,1,3),( 5,2,6),( -2,-1,-3):}] is nilpotent matrix of index 3.

The matrix [(2,lambda,-4),(-1,3,4),(1,-2,-3)] is non singular , if :

If A=[{:(2,-2,-4),(-1," "3," "4),(1,-2,-3):}], show that A^(2)=A.

Express the matrix A={:[(2,-3,4),(-1,4,3),(1,-2,3)]:} as the sum of a symmetric and a skew symmetric matrix

The matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is (A) idempotent matrix (B) involutory matrix (C) nilpotent matrix (D) none of these

The rank of the matrix A={:[(1,2,3,4),(4,3,2,1)]:} , is

Find the adjoint of the matrix: [(1,2),(3,4)]

Express the matrix B=[2,-2,-4-1,3,41,-2,-3] as the sum of a symmetric and a skew symmetric matrix.