3. In M3x2(F), prove that the set (GDCD69(960) { ( ) ( ) ( ) ( 8). 1 is linearly dependent. {}

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

A:

Q: 10) Show that [x] = −[−x] A 11) suppose that g: A → B and f: BC, where A = B = C = {1,2,3,4}, g =…

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Q: .A. Find the domain of the tollowling Fune tions :- 1. Fex) = V4-12X

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 4) [ (2– t)/tdt xdx 5) o Jr+ 2x 2

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Q: then -A U= 4 5 and uTu · [

A: The given matrix

Q: T -2 4 f(x) g(r)|h(r) 5 4 9 2 -3

A:

Q: I have the following example:  "For the function f : A = {a, b, c, d, e} → B = {1, 2,..., 6}…

A:

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: 4. Use rule of inference to show that if Vx(P9x) → (Q(x) ^ S(x))) and Vx(P(x) ^ R(x)) are true, then…

A: Given: Lets determine∀xPx→Qx∧Sx and ∀xPx∧Rx is true and ∀xRx∧Sx is true using rule of interference.

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3,…

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

A:

Q: Example 9. Classify each relation as constant, linear, quadratic, or neither. a) y = x² + 5x + 6 b)…

A: The solution is given below:

Q: Prove the validity of the following arguments Vx, A(x) → B(x) Ex, A(x) ^ C(x) Vx, C(x) →D(x) ..3x,…

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Q: 1 Expand f (z) = in the domain 4 < |z| < 12 (z-4)(z-12)'

A:

Q: IF fx) = (1 - x) and g(x) = 9 - x, find fg(x)) and g(fx)). Ag(x)) = 9(Ax)) =

A: Given that:           f(x)=(1-x)2 and g(x)=9-x Find f(g(x)) and g(f(x)).

Q: What is the relations (5)/(8) and (8)/(10) Drag and drop a tern

A: Ok

Q: Find ƒ(2), ƒ(3), ƒ(4), and ƒ(5) if f is defined recur- sively by f(0) = -1, f(1) = 2, and for n = 1,…

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Q: Oind Let g(2) = u(2)+iv(2) be ol complete function hiC →C, h(2) = e¯( v(a)+iu(2). Show that if h is…

A: gz=uz+ivz is a complete function and h:ℂ→ℂ by hz=e-ziuz+vz is a entire functionTo prove: g is a…

Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

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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: Prove that (+¹)=()+(²1).

A:

Q: *) Let p(x) = 8x – 7 and q(x) = /x – 7. Find u(x) given that q(x) = p(u(x)). - и(x) —

A: see 2nd step

Q: Determne whether the hamit exitis or not when a)x3 and b) x→ -3 x²-9 when x< -3 F(x)= 9-x² when -3<…

A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: 4. Let X1, ,X4 be iid Unif(0, 0). (a) Show that X(4) is independent of X(1)/X(4). (b) Show that X(4)…

A: Given that X1,X2.............,X4 be iid Unif0,θ (a) X4 is complete sufficient statistics and…

Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: 17. Let y₁ = x₁ + x₂ and y₂ = x² + x² + 2(x₁ + x₂ + x₁x₂). (a) Use the Jacobian to test whether…

A:

Q: Let 1 -1 8 -3 -5 2 -1 , and B = 1 %3D %3D -2 1 4 -7 Compute A-1, (BT)-1 and B-1A-1. What do you…

A: A=1-1102-1-213, B=8-3-50124-76 Expanding the determinant of A, B along column first…

Q: 4 [5], 9 (a) Write b as a linear combination of a₁ and a2. Let al b a2 = -8 7 and T(a₂) and b = 2…

A: See below for the complete solution -:

Q: If A is an adjoint operator on H=K2 and  for x=(x(1), x(2)), we define A(x)=(x(1)-x(2), x(1)+x(2)),…

A:

Q: (-8 1 4 (a) If A = 4 4 7 prove that A- = A' where A' is the transpose of A. 1 -8 4

A: