Final answer:
The answer involves evaluating a polynomial function for a square matrix, by substituting the matrix into the function and using matrix operations to compute the result.
Step-by-step explanation:
The question asks to evaluate the function f(a) for a square matrix a when the polynomial function f(x) is given. The polynomial function is expressed as f(x) = a0 + a1x + a2x2 + ... + anxn, where the coefficients a0, a1, ..., an are constants and x is the variable. For a square matrix a, the function f(a) is similarly evaluated as f(a) = a0I + a1a + a2a2 + ... + anan, where I is the identity matrix and the powers of a are obtained by matrix multiplication.
To solve for f(a), one needs to substitute the matrix a into the polynomial function and perform matrix addition and multiplication accordingly. For instance, if we have the polynomial function f(x) = 2 + 3x + 4x2, and a is a given square matrix, then f(a) would be 2I + 3a + 4a2, with the operations applied to matrices.