If find k such that A2 – 8A + kI – 0.
Given:
I is identity matrix, so
Also given,
Now, we will find the matrix for A2, we get
[as cij = ai1b1j + ai2b2j + … + ainbnj]
Now, we will find the matrix for 8A, we get
So,
Substitute corresponding values from eqn(i) and (ii), we get
[as rij = aij + bij + cij],
And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal
Hence,
Therefore, the value of k is 7