3. Given BF is F(x,y,z) = x yz +xyz+ x ỹ z +x yz. (i) Simplify the BF by k-map (ii) Draw a circuit(using inverter, OR, AND gates) and make a truth table of simplified form of BF.

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: 7. Compute the Jacobian of the following transformation. x=u²+uv y=3uv².

A: The given data is: x=u2+uvy=3uv2 To find the Jacobian transformation.

Q: 2) Set up the de finite imtegro gain bat u- substitution and then evaluate it,

A: Evaluate by applying u substitution

Q: * find z- transform for -4 x (n) = { 2 1 2 3} x(2) = 2 +z + 2z-2 + 3z-3 x(2) = 222 + z +=+ 2 + 3Z'…

A:

Q: Suppose you are given four natural numbers w, x, y,z e N such that w>x and y > z. Show that ly – w|…

A: It is given that w, x, y, z are natural numbers such that w>x and y>z. Now we want to show…

Q: 1. To show that the transform x - Ax = (x1- 2.x2 + x3,3x1+ x2,2x2 – x3), = (r1,#2, 13) E R³ is…

A:

Q: Exercise 3.28. It is obvious that if T1 is both coarser and finer than T2 on X, then the topologies…

A: Definition: The topology τ1 is finer than τ2 on X, if τ2⊂τ1. Definition: The topology τ1 is coarser…

Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

A:

Q: of is: If f(z, y, z) = ry z' + In (z) In (y²) In (z³) then dz

A:

Q: Find the infimum and supremum of the set X = {3 – Vztn ine N}. -

A:

Q: in in Signed-Rank Test a two-sided alternative, we may reject H0 in favor of H1 if either w+ or w-,…

A: Signed rank test for  two tailedHo:M≠Mowe reject Ho, if W+≤Wα and W-≤Wα

Q: Calculate the coefficient of x7y5zx7y5z in (x+y+z)13(x+y+z)13. (b) In her discrete math class,…

A:

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: In R, the model mod <- Im(z ~ x + y) will contain: O the results from regressing the dependent…

A: Introduction: It is required to identify the correct option.

Q: 1. Find the Wronskian for yi = x , y2 = x² and y3 = x³.

A:

Q: What is the z transform of x(n) = 25(n+ 1)+ 7õ(n)+ 55(n – 1) + 20(n – 2) 2z + 7+ 5z-1+ 2z-2 2z + 7+…

A:

Q: X1,, Xn ~ N(-3,2) (random variables) ... Z, = 1(X,X2 + X1X3 + X1X4 + •..+ X1X„), n > 3 %3D (a) Find…

A: From the given information, X1, .....,Xn~N-3,2 And Zn=1nX1X2+X1X3+...+X1Xn, n≥3 Consider,…

Q: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

A:

Q: Find {2), f3), R4), and {5) if fis defined recursively by f0) = -1, A1) = 2, and {(+1) = Jtn}*s(n –…

A:

Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

A:

Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: Find Z-transform and ROC f x(n) = {1,2,−1,2,−1}

A: Given that: xn=1,2,-1,2,-1 The objective is to determine Z-transform and ROC. Let consider,…

Q: 6.Use.chain.Rule.to.frind.E GV. ... 2Sin.x.Eoguy Xロサ.……4こ… ...... .......

A:

Q: 1- Find Z-transform if x (n) = bln|

A: The given function is xn=bn To find its Z-transform.

Q: 4. Prove C(n, r) = C(n- 1,r- 1) +C(n- 1, r) %3D using a combinatorial proof.

A: We know, C(n,r) = n!/((n-r)!r!)

Q: What is the Increasing,Decreasing, and Constant Therom

A: Definition of increasing, decreasing and constant theorem

Q: Prove that K4 is not outerplanar

A: In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices…

Q: . Give the Dedekind cuts in R 20 corresponding to the following. Your definition should not refer to…

A: Given: 10 23 23+3 To find: Dedekind cuts in ℝ≥0 for the given real numbers.

Q: let z- 5 dy By chain Ruie

A: Given z = √x dy/dx = (1/2√x)•(dy/dz) We have to find d2y/dx2 .

Q: (3) Recall that a lattice path on the grid from (0,0) to (n, n) can be viewed as a sequence of…

A: Given: To show that Cn,  is equal to the number of ways of placing n unlabelled ball in n labeled…

Q: 19/156) If WG, g) is the Wronskian W(u, v) of u and v in terms of W(f, g). the Wronskian off and g,…

A:

Q: If u=u(y-x/xy,z-x/xz) prove tha x^delu/delx+y^delu/dely+z^delu/delz=0

A: Consider the equation

Q: (a, 0) is not measurable.

A: In this question, we check the given set is measurable or not. here we use the condition of Lebesgue…

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: Prove that a random q-ary code with rate R > 0 with high probability has relative distance 8 2 H,'…

A: Given:: Prove that a random q-ary code with rate R&gt;0 with high probability has relative distance…

Q: Compute the convolution x[n]*h[n] for all n> 0, by using Graphical or Tabular method. x[0] = 3, x[1]…

A:

Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: 7, SHOW THAT FOR EVERY 2x2 DETERNINAAT ANO CONSTANT K THAT! det (KA) = K²det lA)

A:

Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: 2. Suppose that {v1,... , Vp} is an orthonormal set in R", and that x E R". What can you say about…

A:

Q: Construct circuits from inverters, AND gates, and OR gates to produce the output (x + yz)(xy + z).

A:

Q: Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn…

A:

Q: Oct 31, 2021, 16:44 Problem-2 0 Let foo = x?-2a and gcauz VI-x 6) is q CG (-Z)) defined! domain ind…

A:

Q: Illustrate the key ideas in the proof of Hall's Matching Theorem.

A:

Q: Find the first devdivative 2. 2. u = x2+ 2 ut1 %1 ).

A:

Q: 13. If w(x,y) = In(1+xy²), show that 2wxx + y³Wyx = 0. %3|

A: Given: w(x, y)=ln(1+xy2)  To show: 2wxx+y3wyx=0 Chain rule : ddx(f(g(x))=f'(g(x))g'(x) Quotient…

Q: -. Show that both R and R2 may be covered by countably many open balls.

A: Soution.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.