Determine the causal signal x(n) if its z-transform X (z) is given by: 1+3;-! 1+3:-1 +2:-2 (a) X(z) = (b) X(z) = 1-2 (c) X(z) = 1+2;-2 1+:-2 (d) X(z) = 1+6;¬1+;-2 (e) X(z) = i1– 2:-1 +2:¬2)(1 – 0.5z-1) (f) X(z) = 2-1.5:-1 1-1.5:-1+0.5z-2

Q: Prove that Ją (2) = =- J¼ (2) – J_4 (=)

A:

Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

A:

Q: If f is invertible and f(- 15) = 6, then %3D | f-(6) and (f( – 15))¯ -1 %3D

A:

Q: a) f(x) = {(3, –4), (2, 1), (–9,–3)} |

A: We have to find domain and range

Q: (a) (b) W₁ = 4x1 + 5x2 W₂ = x1 - 8x2 W₁ = 5x1 - 7x2 W2 = = 6x1 + x2 W3 = 2x1 + 3x2

A: Given that (a)             w1 =4x1 + 5x2            w2 = x1 − 8x2   (b)            w1 = 5x1 − 7x2…

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: Show that the Newton divided-difference polynomials 3 – 2(x + 1) + 0(x + 1)x + (x + 1)x(x – 1) and…

A: Given: Let P(x)=3-2x+1+0x+1x+x+1xx-1    Q(x)=-1+4x+2-3x+2x+1+x+2x+1x

Q: 7. Find f(4) if f is defined recursively by f(0) = 2, f(1) = 3 and f(n+ 1) 4f(n) -3f(n-1)

A: To find: The value of f (4).Given: The recursive function is defined as

Q: (-5, 2). (3, -2) in z11 x Z4 is (0 ,5) (1 (3,0) (2 (3,5) None 4 3.

A: We have to find the element -5,2·3,-2 in Z11×Z4.