If and then find λ so that A 2 = 5A + λI.

Question

Philoid · Accepted Answer

Given: , and

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

[as c_ij = a_i1b_1j + a_i2b_2j + … + a_inb_nj]

Now, we will find the matrix for 5A, we get

So,

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

[as r_ij = a_ij + b_ij + c_ij]

And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal,

Hence, and

So the value of λ so that is – 7

If and then find λ so that A2 = 5A + λI.