If find f(A), where f(x) = x 2 – 2x + 3.

Question

Philoid · Accepted Answer

Given : and f(x) = x² – 2x + 3.

Matrix A is of order 2 2.

To find : f(A)

Formula used :

Where c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

A² is a matrix of order 2 x 2.

f(x) = x² – 2x + 3

f(A) = A² – 2A + 3I

A² = =

A² =

2A = 2 × =

2A =

3I = 3 × =

3I =

f(A) = A² – 2A + 3I = + =

f(A) = A² – 2A + 3I =