Q. 315.0( 1 Vote )

Show that the matrix satisfies the equation A3 – 4A2 + A = 0.

Answer :

Given:


To show that


Now, we will find the matrix for A2, we get




[as cij = ai1b1j + ai2b2j + … + ainbnj]




Now, we will find the matrix for A3, we get






So,



Substitute corresponding values from eqn(i) and (ii), we get






[as rij = aij + bij + cij]



Therefore,


Hence matrix A satisfies the given equation.


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