Assuming that all matrices are n x n and invertible, solve for D. BCAT DCBTA = BCT. OD = C-¹A BA-¹ (B7)¯'A-¹ OD = (B7) ¹A-CA-¹ (B7) C-¹ OD = (CT) CBTA (CT)-¹B-¹ OD= ATC-¹B-A-BTC-1 OD= (AT) C-CT A-¹ (B¹) C-1

Q: Find the Inverse Laplace of F(s) = S+4 s²+8s+4

A:

Q: Find the formula for the number of ways for putting n identical balls into k distinct boxes so that…

A: Answer is given using concept of permutations and combinations.

Q: Ex: S=28a, 106,5c? How many 5-perm. of 5 are there? k=3, r=5 => 35

A: As per the Bartleby guideline, 1 question can be answered. Please repost the second question.

Q: e. Discuss the solutions to the differential equation. What are the equilibrium points of the model?…

A:

Q: On the set Rwe have two binary operations *aogiven by regulations: a*b = 2 a. b a ob = a + b find…

A: Solution of the given problem is below...

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Given, plane1 =>kx+2y-2kz+3=0 and plane2 => x-2ky+5z=0

Q: Q #2. Explain how the graph of g is obtained from the graph of f. Graph both f and g on the same…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function: y=f(x)±n.…

Q: 2 if A= /3 12 If 057 9 1-4, B- 30 -1 4-62 that i) A+B = 1/2 (2A + 2B :') (AB)" =B³A² ii) -1 "A")…

A: Addition of matrix is defined if the matrices are of same order and is obtained by adding…

Q: VI. Disprove the following statements by providing a counterexample. Use 2 = {1,2,3,4) as the…

A:

Q: 8. f(x, y) = (x³ + (y/2))²/3 10. f(x, y) = x/(x² + y²)

A:

Q: We have a semigroup (M, *), where M = R- {k} a a b = a + b-kab. Find also that, (M, *) is a group.…

A: Semi group will be a group if there exist an identity element and every element has inverse.

Q: find solution using direct integral method for the partial differential equation below: 2³ z 1 = 12…

A:

Q: = 72. P(₁,1) and P(r2, 82) represent the same point in polar coordinates, then ri

A:

Q: Set up the definite integral for the volume of the solid generated when region C is revolved about…

A: To find the volume of the solid generated when region C is revolved about the y-axis, we shall use…

Q: 1. Let lim ||fn - f|| ₁² (1) = 0 n-00 Where I = [0,1]. Show that: lim | fn9ndμ = √fgdµ n-00 I and…

A:

Q: prove that they are not isomorphic by finding an invariant. a to w w wie e Bio are de motor i te mo

A: This is a problem of Graph Theory.

Q: a²0 For 0 = 5a + 3 ln(3a + 5b), solve for дадь Express your final answer as one rational expression.

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Using integration by parts, rewrite the following integral as fudv-uv-fvdu [In (2x) 4x² dx

A: Select the functions: u, dv for the expression: ∫ln2x6e4x2dx and then use the integration by parts…

Q: [2] Determine homogeneous the roots of the auxiliary equation y=x²-ecosx for a linear equation with…

A:

Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

A:

Q: A limacon with a dent symmetric to the polar axis, and points to the left. the left. A cardioid…

A: We have to solve given problems:

Q: nge receives an average in a given minute, the e calls;

A:

Q: Q.7 (a) Obtain the Fourier series of the function f(x) (b) Show that, fcdu=e¹.x > 0. = {1,05x5

A: Using the Fourier cosine integral representation for the result of (b)

Q: Exercises Determine the critical points and locate any relative minima, maxima and saddle points of…

A:

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+32) sin(t)dt

A: we have to evaluate given integral by tabluar method ∫(t3-4t2+5t+32)sin(t)dt

Q: (3) Find the formula for the number of ways for putting n identical balls into k distinct boxes so…

A:

Q: (A) 87632 (D) 98301 (B) 97531 (C) 98532 101 17. 5. HDDAB 84412 (A) 83312 (D) 844 (B) 84312 (C) 74412…

A:

Q: Let {f} is sequence of measurable functions Let there exists F = { x: limf, (x) E } 1-00 Show that…

A: see my solution

Q: Let X = {6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z e N₁ x + z = y}, where…

A:

Q: 3.4.4 Evaluate ff sin(x + y) dx dy over the triangle whose vertices are (0, 0), (2, 1), (1, 2).

A:

Q: a. Consider the function f(x, y) = ex²-² 1 1 i. Sketch level curves f(x, y) = k for k = and 1 on the…

A:

Q: Let X= (6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z e N, x + z = y}, where…

A:

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

A:

Q: 2. An oven technician charges a call-out fee of $50 and an additional $20 per hour for the duration…

A: The call out fee is $50 additional fee per hour = $20 per hour let t be the number of hours…

Q: 1. Solve the difference x²-2x-8 < 0.

A: Solution of the difference equation

Q: 4-G Given that A= (1) AB (ii) B (iii) AT 1-2 1 3 5 0 2 06 and B-3 1 2, determine 4-13,

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…

Q: 3.4.4 Sketch the domain of integration and evaluate 2x 1-x dy (a) dx (b) Laxf d.x 2 Xx² + y²² dx dy…

A:

Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

A:

Q: 5. y"+y' - 2y = 54te-2t, where y(0) = 6, y'(0) = 0

A:

Q: Which of the following sets is linearly independent? -ex-y-5=x+C OM= {(1,3),(3,9),(-1,-3)) M=…

A:

Q: The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

A: The volume: V of a cylinder is calculated using the formula: V=πr2h, where r is the radius and h is…

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Given planes are kx +2y -2kz +3 =0x -2ky +5z =0   Rewrite the equation: kx +2y -2kz  =-3  x -2ky +5z…

Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

A:

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x- 2ky + 5z = 0…

A:

Q: to evaluate the following: - f(t³-4t² + 5t+ 32)sin(t)dt (B) Use Tabular integration

A: By using tabular integration , integrate the given problem...

Q: 1. Consider the system of linear equations below: 5x-4y+2z=21 -x-5y+6z=-24 -x-4y+5z=-21 a. Solve the…

A:

Q: y' - 2x²y = -x =−x

A: We have to solve given problems:

Q: Directions: Translate each argument into symbolic form (using the suggested letters) and determine…

A: A mathematical argument can be expressed by using the symbolic form. Each simple component of the…

Q: [4] Let f(x) = = {₁2 of f. (b) (c) (d) Sketch the odd periodic extension of f. 1 (e) Find the…

A: The given problem is to find the Fourier sine series of given periodic function with given period.