Suppose A is a 5 by 5 matrix. Its entries in row 1 multiply determinants (cofactors) in rows 2-5 to give the determinant. Can you guess a "Jacobi formula" for det A using 2 by 2 determinants from rows 1-2 times 3 by 3 determinants from rows 3-5? Test your formula on the -1, 2, -1 tridiagonal matrix that has determinant= 6.

Q: Give an example of a conditionally convergent series an such that Σna, con- n=1 n=1 verges.

A:

Q: f(t) = 5e-2t + calculate the LT. +² 2'

A: Laplace transformation of the function

Q: In part(a),If I use the mathematics induction,should I suppose that i=n-1 is true?

A: Mathematical induction is a method to prove any statement true for all natural numbers.  It starts…

Q: A rational number is a real number which can be written as the fraction of two integers. Which of…

A: The objective is to choose the correct form of Rationalx. In words, for any real number x, Rationalx…

Q: 3. Give the lattice of subgroups of Z₂ x Z4.

A: The objective is to evaluate the lattice subgroups of ℤ2×ℤ4. The group ℤ2,+2 is given as 0,1. The…

Q: Find the angle at which the circles x² + y² + x + y = 0 and x² + y² + x − y = 0 ir If the circles x²…

A: The angle of intersection of the two circles is given by cosθ=r12+r22-C1C22r1r2where r1 and r2 are…

Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

A: Given, the initial temperature (T1)=310o k initial Pressure (P1)=18  atm Initial volume V1 = 120 lit…

Q: Problem 8: Let V be finite-dimensional and let U be a subspace of V. Let Prʊ € L(V) be the…

A: Sol:- To show that Pru* = Pru, we need to show that for any x, y in V, we have ⟨Prux, y⟩ = ⟨x,…

Q: prove that each wff is a valid argument. (∀x)P(x) ^ (∃x)Q(x)  → (∃x)[P(x) ^ Q(x)]

A: Given: ∀xPx∧∃xQx→∃xPx∧Qx We have to prove that the given wff is a valid argument.

Q: nd the condit. on if the circle whose equation a x² + y² + c² = 2ax = 0 and x² + y² + c² = 2b y = 0…

A: The two circles are x2+y2+c2=2ax=0 and x2+y2+c2=2by=0.centers:C1(a,0),C2(0,b)radii:r1=a2=c2,r2=b2-c2

Q: 24. If a and b are distinct group elements, prove that either a² + b² or a³ + b³.

A:

Q: . Let y be the boundary of the rectangle whose vertices are at 2+ i,-1+i, -1-3i, and 2 - 3i…

A:

Q: 5. Let V be a finite-dimensional F-vector space, and let {₁,...,Um} be a set of m vectors in V. Show…

A: Sol:- To show that (a) and (b) are equivalent, we need to show that if (a) is true, then (b) is…

Q: Maria, who is now 49 years old, is employed by a firm that guarantees her a pension of $45,000/year…

A: Sol:- The present value of a continuous annuity can be calculated using the formula: PV = C / (r -…

Q: 3. Consider the plane P: 6x + 3y + 2z = 6. o(a) Draw the first octant of this plane in the graph…

A: The equation of the given plane is P: 6x+3y+2z=6 The given region is R=0,0.5×0.5,1 in the xy-plane.…

Q: Two adjacent vertices of a square are (1,2) and (-2,6).Find the other vertices. Find the distance…

A: Given two adjacent vertices are A(1,2) and B(-2,6).then,AB=5Also,the slope of AB…

Q: Let an = n 2i - 1 2i where n is a positive integer. i=1 (a) Find a1, a2, a3 and a4. (b) Guess a…

A: Given: Let we have an=∑i=1n2i-12i Here n is an positive integer. we have to find: a) a1, a2, a3 and…

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A:

Q: A straight line is drawn through the point P(2,3) and is inclined at an angle of 30\power{∘} with…

A: Here,(x1,y1)=(2,3),θ=30°.the equation of the line is x-2cos 30°=y-3sin 30°or  x-23/2=y-31/2or…

Q: Problem 7: Let €1, €2, . . . , ¤n,…. be an infinite list of orthonormal vectors in V. Let v ¤ V and…

A: There are two parts to the question. In the first part, it is required to show that ∑i=1∞ai2…

Q: Determine the diameter of the set U = (9, 14) U (22,31) in the metric space R with metric being the…

A:

Q: Express the given complex number in polar form. [1(cos(3)+ i sin()) [2(cos() + + sin(+))] ¹0 10

A: We know that eiθ=cosθ+isinθ and eiθn=einθ ∀n∈ℤ .

Q: 9. Given that y = ce cos x + ce sin x is a two-paramet solutions of y" - 2y' + 2y = 0 on the…

A: As per our guidelines we can answer only first question and rest can be reposted.  Here we have to…

Q: a b с 1 0 10 0 10 0 1 0 2= = ab + c Z Delete selected item(s) Undo 104 Click to add.

A:

Q: Let {n} be a Cauchy sequence. Prove that {s} is bounded.

A: Given: In this question, the given details are, Let {sn} be a Cauchy sequence. To Prove that {sn} is…

Q: 8. Let S (12345), T = (13)(45) in S5. Describe the group generated by S and T? =

A: Given ,  S=1 2 3 4 5  and  T=(1 3)(4 5) in  S5 . Then we find group generated by  S and T .

Q: Problem 12. Find the matrix A which takes a vector (x, y, z) into (y - x, zy, -2). This matrix is…

A:

Q: Four people are running for class president: Liz, Fred, Sue, and Tom. The probabilities of Fred,…

A: we need to find probability that  a) Liz wins b)Fred or Tom wins c)Tom loses

Q: A local travels company is in the business of car rentals. Due to covid, pricing of the car rentals…

A:

Q: A vector field is defined in spherical coordinates by (₁0,0)=re, +²sin deg + rep What option gives…

A:

Q: Write the dot product of (1, 4, 5) and (x, y, z) as a matrix multiplication Ax. The matrix A has one…

A: Given, A=145, x=xyz Ax=0

Q: The object shown in the figure is axially symmetric and its curved surface is described in…

A:

Q: The equation y'-y = 4te is a first order linear DE in standard form. O True O False

A:

Q: 1. An ellipsoid is created by rotating the ellipse 4x² + 2² = 16 and the z-axis. Find an equation of…

A:

Q: 4. If it is a dog, then it has fleas. It has fleas. Therefore, it is a dog. 5. If we serve salmon,…

A: We need to determine the argument is valid or not.

Q: Give an example of ring elements a and b with the properties thatab = 0 but ba ≠ 0.

A: We have to give the example of ring elements that follow the following properties: ab=0 but ba≠0.

Q: Having received a large inheritance, Jing-mei's parents wish to establish a trust for her college…

A:

Q: what is the negation of 2+1

A: We have 2+1=3.

Q: Newton's law of cooling states that the rate of change in the temperature T(t) of a body is…

A: Given Data: Newton's law of cooling states that the rate of change in the temperature​ T(t) of a…

Q: The line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction…

A: The slope m of the line AB is given by        m1-03-2=1So,AB makes an angle of 45° with the…

Q: dp dt The logistic equation for the population (in thousands) of a certain species is given by…

A:

Q: Use cylindrical shells to find the volume formed by rotating the region in the first quadrant…

A:

Q: Problem 5: Suppose V is finite-dimensional and P € L(V) is such that P² = P and that every vector in…

A: Given: Let consider V is finite-dimensional andP∈L(V) is such that P2=p. We have to show that P=Pru.

Q: Apply the Adams third-order predictor-corrector method (by hand) to approximate the solutions for…

A: Sol:- The Adams third-order predictor-corrector method is a method for numerically approximating the…

Q: Anna spends R200 on prepaid electricity at the start of the month. Joe buys R30 of electricity every…

A: Given: Expenditure of Anna and Joe on electricity.To find: The better deal among both.

Q: E is the elementary matrix obtained by interchanging two rows in In. A is an n × n matrix. (a) How…

A: Given: E is the elementary matrix obtained by interchanging two rows in In. A is a n×nmatrix. To Do:…

Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤T/2, dr do -8…

A: The given curve is: r=8cosθ;  0≤θ≤π2. To Do: Find the derivative drdθ. Compute the surfaced area…

Q: Let f(z) = 1 (z − 1)(z − 2)(z − 3) - Calculate the Laurent series expansion about z = 0 of f(z) on…

A:

Q: Determine if b is in the span of the other given vectors. If so, express b as a linear combination…

A:

Q: Use matrices to prove the given state­ments a bout transformations from R2 to R2. If Rθ denotes a…

A: To prove the statement using matrices, we need to represent the transformations in matrix form. The…