Question: (a) Let f: R4 R be a linear mapping defined by f(x, y, z,t) = (x-y+z+t, 2x-2y + 3z + 4t, 3x + 3y+4z

(a) Let f: R4 R be a linear mapping defined by f(x,

(a) Let f: R4 R be a linear mapping defined by f(x, y, z,t) = (x-y+z+t, 2x-2y + 3z + 4t, 3x + 3y+4z + 5t). Find the rank and nullity of f (b) Let A be an n-square matrix. Define diagonalization of A in: (i) matrix point of view (ii) linear operator point of view (c) Define characteristic polynomial of a square matrix A. Hence, 1 2 3 find the characteristic polynomial of A = 30 4 6 4 5

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