Q. 204.8( 5 Votes )

If then show that A is a root of the polynomial f(x) = x3 – 6x2 + 7x + 2.

Answer :

Given: and f(x) = x3 – 6x2 + 7x + 2


To find the value of f(A)


We will substitute x = A in the given equation we get


f(A) = A3 – 6A2 + 7A + 2I……………..(i)


Here I is identity matrix


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) in equation f(A) = A3 – 6A2 + 7A + 2I, we get






[as rij = aij + bij + cij],



Hence the A is the root of the given polynomial.

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