1.36 (a) Show that any set of four vectors in R2 is linearly dependent. (b) Is this true for any set of five? Any set of three? (c) What is the most number of elements that a linearly independent subset of R? can have?

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy dA ax ду for the given path. C:…

A:

Q: itely generated projective modules over a local ring are free. jective modules are flat, but the…

A: Sol

Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P'AP gives the proper…

A: As this problem is related to orthogonal diagnolization of a matrix, hope you know how to find…

Q: 3. 2х, X2 = 2 4. 4x, + х х, — Зх, + х; 3 —2 -x, + x2 - 3xz x – 7x 3x1

A: Q3 asked and answered.

Q: A bacteria culture initially contains 1600 bacteria and doubles every half an hour. Find the size of…

A: Solution:

Q: Ex - 9

A:

Q: There are 10 people in a dinner gathering. In how many ways can they arrange themselves around a…

A: We have to find the correct option from the given options.

Q: -3 Given v = 9 10 find the coordinates for v in the subspace W spanned by 2 1 4 u1 = 2 U2 = and uz…

A:

Q: eated by connecting NW and NE strands to ch other and connecting SW and SE strands gether. C^ may be…

A: Sol

Q: Suppose you are producing an outdoor festival. You estimate that you will make $300000 if it does…

A: We have to find what are expected earnings for the festival.

Q: = e* sin dx2 dx dy + 4x dx 3. Solve the Cauchy-Euler equation x 2 d?y + 2y e*. 4. Evaluate (cin t…

A:

Q: Write the statement in words if: p: Firemen work hard. q: Firemen wear red suspenders 4) ~(q ⋁ p)

A:

Q: Q4) Find plane area inside polar function r 2 and outside polar function r = -2sine in third…

A:

Q: 1. Solve by D operator method d?y 2y+y = x²e3x dy dx2 dx Sol

A:

Q: Find the Inverse Laplace Transform of the following functions 1 2) F(s) = s'+4s

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. Use Laplace transforms to solve the initial value problem, 4t, 0<t<1 y' +2y = f(t), y(0) = 0,…

A:

Q: An Jibble is produced on an assembly line consisting of six workstations. The total work content for…

A: Total time = 22 minutes Maximum time of workstation = 6.5 minutes Operating efficiency = 120% Cycle…

Q: 2y+y = x²e 3x. d?y thod - dx2 2. Solve by method of variation of parameter - 2 = ex sin x. %3D dx?…

A: Solution by a variation parameter method

Q: Find the eigenvalues A1 < A2 and associated unit eigenvectors ü1, ủg of the symmetric matrix 7 61 A…

A:

Q: Aunt May recently learned about discrete probability. She performed a random experiment of rolling a…

A: Total number ofoutcome for rolling a die three times = 6×6×6 = 216

Q: A ball with mass 0,15kg is thrown upward with initial velocity 20 m/s from the roof of a building…

A: Find the maximum height above the ground the ball reaches. The right model is now…

Q: a) Find the number of walks of length 3 between each distinct pair of vertices. b) There is 1 walk…

A:

Q: 3. Solve the Cauchy-Euler equation x + 4x+ 2y = e*. ax dy 4. Evaluate L (sin t- cos t)?. dx2 dx

A: Cauchy differential equation and it's solution

Q: x3 – 2x? – 5 = 0, [1,4]

A: The given equation is x3-2x2-5=0. We have to find the root of that equation by Newton -Raphson…

Q: Use Gram-Schmidt to find q1, q2, q3 (orthonormal) as combinations of a, b, c (independent columns).…

A:

Q: Question 2: The velocity of a dragster t sec after leaving the starting line is 100te -0.2t ft/sec.…

A:

Q: producf inner Give the definition of the complex space.

A: In this question we have to give the definition of complex inner product space.

Q: Using Legendra polynomia lsFind 9quadratic least-square approximation For cosh Cx)

A: We have , fx = coshx We know that , the quadratic approximation of  least square polynomial is given…

Q: Write an equation for the function graphed below. Use the smallest powers possible to meet the…

A:

Q: Draw a tree on 6 vertices where all but one vertex has degree 1.

A:

Q: H. What scale is Used if a bine 81 mm fence G3 m fang? fay epreenți पंपम्कैय विषे

A: The ratio of the length in a drawing (or model) to the length on the actual thing is called scale.…

Q: -3 Given v = -6 find the coordinates for v in the subspace W spanned by -7 -4 -1 2 3 -2 1 U2 = 1 ,…

A:

Q: Jesaki Express, a national package delivery service, charges a base price for overnight delivery of…

A: Given that,The service charges a base price for overnight delivery ofpackages weighing 1 pounds or…

Q: A fair die is rolled four times. What is the probability of obtaining a 5, 3, 5, and 5, in that​…

A:

Q: I. Use Gauss-Jordan elimination to transform the matrix in reduced row echelon form. 1 -3 -6 5 -21 2…

A:

Q: (x – 2)? – In x = 0, [1,2]

A: Sol

Q: Laplace transform to solve the given initial-value problemn. y"+ 2y" y' 2y – sin(3t), y(0) = 0 y'0)…

A:

Q: Which of the following expressions represents the number of distinguishable permutations of the…

A: We want to find total number of permutations of word CONCLUSIONS

Q: The daily cost, in dollars, to produce x gallons of handmade ice cream is C(x) = 1.3x + 11. The…

A:

Q: 1. Solve by D operator method dx2 +y = x e dx

A:

Q: A Math class consists of 14 girls and 15 boys. The teacher randomly selects 6 students to show their…

A:

Q: Evaluate the following integral "/2 (8 + 4cosx)dx a. Single application of the trapezoidal rule b.…

A:

Q: Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

A:

Q: A survey of students to determine if they had a pierced ear was given. The results are summarized in…

A: Concept: Probablity=Total favourable outcomestotal outcomes

Q: Spanning Trees Create 2 different spanning trees of the following graph.

A:

Q: Given the popula 1950 to Year 1940 1960 1970 :066T 1980 1990 Population 132,165 in 203,302 226,542…

A: Given: Year Population 1940 132165 1950 151326 1960 179323 1970 203302 1980 226542…

Q: Find the vertex set, edge set, and edge endpoint table of the digraph G. e1 V2 V1 e5 e6 ez e7 e4 e8

A: Given a graph with edges and vertices as shown above. To find the vertex set, edge set and edge end…

Q: L(eT+h) = ae?+h +h = YT+h - ÎT+n/T. Assuming that YT+h~N(µr+h»o%+n}; show that the optimal s equal…

A: Sol

Q: The Inverse Laplace Transform for 1/S-3 is u(t)e^3t e^-at t^2 t

A:

Q: QUESTION 4 Let V be a vector space of dimension 2n > 2 over R. (4.1) Show that a complex scalar…

A: