A matrix M is said to be orthogonal if MMT=MTM=1. Let S be a skew-symmetric matrix and I the identity matrix. If I-S is invertible, can we say that the matrix A=(I + S) (I-S) is orthogonal?

Q: Show that if 4, and A, are two events, then P(A₂)+P(A₂)−1≤P(44₂).

A: First we will write Inclusion-exclusion principle for two sets.

Q: Find the optimal solution of the following (T.P) by using Least-Cost method. 6 40 50 70 90 90 100…

A: Given,   W1 W2 W3 W4 W5 supply F1 (4) (1) (2) (6) (9) 100 F2 (6) (4) (3) (5) (7) 120 F3 (5)…

Q: Design the network represents the following activities, then find the critical path. M) activity…

A:

Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

A:

Q: e-3t sin (4t) y (0) ==

A:

Q: III. What is the image of the line with equation Y = 5X + 7 under op, where P = (-3,2).

A: Dear Student, Since you have asked multiple questions, we will solve the second question for you. If…

Q: x(n)= a"u(k − n) for k>0

A: Introduction: The Z-transform translates a discrete-time signal, which is a sequence of real or…

Q: 1. Describe the transformations of the graph of y=x to obtain the graphs of the following functions.…

A: Given: y=x To find: The transformations used to get the equation y+4=-2x

Q: ) Solve by using Laplace transform the partial differential equation ay-9 0² =0 dy(x,0) y(0,t)= 0,…

A:

Q: Q4: Solve the following differential equation using Laplace transform d²y 1. + 25y = 10 (cos(5t) - 2…

A: Solution:-

Q: Let V, W be two matrices of the same order. If all entries of V are nonzero, then we say that X is…

A:

Q: Homework for Newton-Raphson 1. Find the positive solution of 2cos x = x until you find the six…

A: # as per the guidelines we are entitled to solve one question at a time ,please resubmit the other…

Q: Using a binomial approach, find the sum S given by n+1 S="C₁ + "+¹C₁ + "+2² C₂+...+ "*C,

A: Here we can use the following formula to find the sum nCr+nCr+1=n+1Cr+1and nC0=1

Q: If A, B, C are sets, show that a) Ax B=0 ⇒ A=0 or B = 0). b) (AUB) x C = (AXC) U (BxC). c) (An B) x…

A:

Q: Show that the quadrilateral having vertices at (1, −2, 3), (4, 3, −1), (2, 2, 1) and (5, 7, −3) is a…

A:

Q: Test the convergence of the following: 1- a. -(3n+1)*

A:

Q: A function u = f(x, y) with continuous second partial derivatives satisfying Laplace's equation…

A: Solution

Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

A:

Q: Describe the surface with cylindrical equation r=6. Hint The 8 and 2 components of points on the…

A: We have to find the surface whose cylindrical equation is given by: r = 6.

Q: etermine the constant a so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal.

A: Solenoidal vector field

Q: 6. Suppose A = (3, -2, 4), B = (-5, 7, 2) and C = (4, 6, -1), find A × B.A+B-C.

A:

Q: If z₁ = 13-101 and 22-15 +91, determine the following: 42₁-522 (Polar Form) COMPLETE THE MISSING THE…

A: We have z1=13-10i , z2=-15+9i Consider: 4z1-5z2=413-10i-5-15+9i=52-40i+75-45i=127-85i Hence,…

Q: 3) Determine the rule writing it below and then complete the tablic 3

A:

Q: Solve the following system using the Newton-Raphson method for one iteration, given that…

A:

Q: Fitting plungers into holes A random variable X has a N(p., o) distribution. Independently, a random…

A:

Q: Be sure to show all work and all problem solving strategies. Give complete explanations for each…

A: Solution : a) X1 matrix is product of A and X where, X1(i,1)=Ai1X0(11)+Ai2X0(21)+Ai3X0(31) where,…

Q: Paul and Eric are playing squash, and Paul is determined to win at least two games. Unfortunately…

A:

Q: calculate the volume of G where G is bounded by 2= x² + y²₁ ²²+ y² = 4, 200 SS f d v

A:

Q: Find (2) and (7) at the point (w, x, y, z) = (48,1, -2,-2) if w=3x²y² + 3yz - 3z³ and x² + y² + z² =…

A:

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7, 8) leave exactly 1 element fixed?

A:

Q: Find the basic solution for the following (T. d the optimal solution. 4 1 2 6 9 100 4 3 5 7 120 2 6…

A: Check if the problem is balanced by finding the sum of rows and columns 100+120+120=340…

Q: b, be complex numbers and N a positive natural number such N¬I i2knx N = απ Τ n = 0 to N - 1 k=0

A:

Q: Find all possible values of a e and Iz+2a-(a + 1)i> 3 simult

A:

Q: Use Laplace transform to solve the partial differential equation: 8² y dy = +xt where y(x,0) = 0,…

A: Solution

Q: (-) 2 _x(n) =| n [u(n)—u(n–10)]

A:

Q: 2. If f(x, y) = log (x² + y²), then ƒ + fyy is equal to 1 (a) x² + 2 (b) 0 + y 2 x² - y² y²-x² (c)…

A: We need to find the partial derivatives fxx , fyy  of the function f(x, y)=log(x2+y2) to find fxx +…

Q: Use the given graph to estimate the value of each derivative. ya y = f(x) 0 1 (a) f'(0) 1 (b) f'(1)…

A:

Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

A:

Q: Use Laplace transform to solve the partial differential equation: o'y dy = dx² dt -+xt where y(x,0)…

A: Consider the given partial differential equation, ∂2y∂x2=∂y∂x+xt where yx,0=0, y0,t=0 and t>0,…

Q: Recall, you own 9 regular ties and 7 bow ties. You realize that it would be okay to wear more than…

A:

Q: Let f(x, y, z) = 9 (√√x² + y² + 2²), where g is some nonnegative function of one variable such that…

A: In the given problem, we calculated the norm and the mass of the given surface. The detailed…

Q: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the given graph the four vertices A, B, E and F are of odd degree,hence by the Eulerian Graph…

Q: 6-

A:

Q: Q3: Find f(t) (Inverse Laplace Transform )of the following functions nn 1. F(s) = 2.F(s) = s+1 s4+5²…

A:

Q: SD a strongly connected graph? D: W

A:

Q: 2. Find the eigenvalues and eigenvectors of A = 2 1 0 121 O 1 2

A: Solution :-

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

Q: S 5 1 1

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the graph given in question each vertex has a degree of 4, hence from the Eulerian Graph…