If f(x) = x3 + 4x2 – x, find f(A), where

Q43 of 307 Page 5

If f(x) = x³ + 4x² – x, find f(A), where

Given: and f(x) = x³ + 4x² – x

To find the value of f(A)

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

f(A) = A³ + 4A² – A ……………..(i)

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 A³, we get

So, Substitute corresponding values from eqn(i) and (ii) in equation f(A) = A³ + 4A² – A, we get

[as r_ij = a_ij + b_ij + c_ij],

Hence the value of

If compute A² – 4A + 3I₃.

If f(x) = x² – 2x, find f(A), where

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

If then prove that A² – 4A – 5I = 0.