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Find the solution of the recurrence relation \[a_n = 3a_{n-1} – 3a_{n-2} + a_{n-3}\] if\[a_0 = 2,\quad a_1 = 2,\quad a_2 = 4.\]
State inclusion-exclusion principle. For which number x is true that\[\lfloor x \rfloor = \lceil x \rceil\] ?Let f and g be functions from {1, 2, 3, 4} to {a, b, c, d}, and from {a, b, c, d} to {1, 2, 3, 4}, respectively with f(1) = d, f(2) = c, f(3) = a, and f(4) = b, and g(a) = 2, g(b) = 1, g(c) = 3 and g(d) = 2.
(b) What is rank of a matrix? Find the rank of a matrix A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{bmatrix}
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