Home > Matrix Algebra calculators > is Idempotent Matrix calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find Is Idempotent matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]]

Solution:
Your problem `->` Is Idempotent matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]]


A square matrix `A` is called an idempotent matrix, if `A^2 = A`.


`A` = 
`2``-2``-4`
`-1``3``4`
`1``-2``-3`


`A×A`=
`2``-2``-4`
`-1``3``4`
`1``-2``-3`
×
`2``-2``-4`
`-1``3``4`
`1``-2``-3`


=
`2×2-2×-1-4×1``2×-2-2×3-4×-2``2×-4-2×4-4×-3`
`-1×2+3×-1+4×1``-1×-2+3×3+4×-2``-1×-4+3×4+4×-3`
`1×2-2×-1-3×1``1×-2-2×3-3×-2``1×-4-2×4-3×-3`


=
`4+2-4``-4-6+8``-8-8+12`
`-2-3+4``2+9-8``4+12-12`
`2+2-3``-2-6+6``-4-8+9`


=
`2``-2``-4`
`-1``3``4`
`1``-2``-3`



Here `A^2 = A`, so `A` is an idempotent matrix






Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

Share with your friends, if solutions are helpful to you.
 
Copyright © 2018. All rights reserved. Terms, Privacy