Linear Algebra: State wheether the following statement is true or false with an explanation  Every Homogeneous linear system has a solution

Q: Let F be a field and f(x) e F[x] be a polynomial of degree > 1. If f(a) = 0 for some a e F, then f (...

A: Since α ∈ F, x- α ∈ F[x]. Also f(x) ∈ F[x].

Q: Determine whether the Series is convergest divergent. or write the exact test that you Us e. nt2

A: Series and sequences

Q: Is the thinking illustrated inductive or deductive

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Q: One solution of the differential equation is given. Find the general solution. y)-y"-12y'-40y 0, y e...

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Q: Let X = the integers. Let Y = {0, 1, 2, 3, 4, 5}. %3D Let f : X Y be defined as the remainder when x...

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Q: Evaluate the integral f cos z(1 - sin 1)-1/2 dr. O In (cos r) +C O In (sin z) + C 2-in(1- sin 1) + C...

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Q: 2 Convert this ntegral From rectangular Coordinte to Spherical Coordina tes (Donot eval vate the Eut...

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Q: Consider the region bounded by y = x², y = 9, and the y-axis, for x > 0. Find the volume of the soli...

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Q: E valuate the Following in tegrals: sec (2+) dt tan (2t) 9.

A: Given that  The integral is  To evaluate the integral

Q: Let D = {1, 2, 4} %3D Let P(x) be the predicate "x - 2x 0". Is it true that Vx E D, x- 2x > 0?

A: Proving by counter example.

Q: B.2. Express to its standard form, determine the center, radius ar 10. x² + y? + 10x – 14y + 58 = 0 ...

A: # We are entitled to solve one question at a time , please resubmit the other question if you wish t...

Q: QID You have been given the paraumetric curve shown be low. oc = 6 + 9t°, y= 3+ 6t9 Figure out what ...

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Q: Solution by Gauss seidel method. 15x + 2y – z = -200 2x + 12y + z = -250 1x + 2y + 8z = 30

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Q: Assume that you take out a $2000 loan for 30 months at 9.5% APR. What is the monthly payment - $75.1...

A: It is given that a loan amount of $2000 is received for a time period of 30 months at the rate of 9....

Q: O Convert this Entegral From rectangular Coordinate to Spherical Coordina tes (Donot eval vate the E...

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

Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the...

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.  

Q: Solve the recurrence an= 4an-1- 4an-2, ao=1, a1=1

A: a2= 4a1 - 4a0 So, a2= 4×1 - 4×1=0 Again, a3= 4a2 - 4a1 So, a3=4×0 - 4×1 = -4 Again, a4= 4a3 - 4a2 So...

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n2 +2...

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Q: This is one question but I couldn't fit the whole question in one photo so I attached two photos, th...

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Q: a) Prove that S is a subspace of R', find the dimension and two basis B1 and B2; 1. Consider the set...

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question...

Q: Differentiate a circle from a parabola?

A: A circle is (geometry) a two-dimensional geometric figure, a line, consisting of the set of all thos...

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: Consider the solid Q that is generated in the first octant by the surfaces S1 : y+z = 4, S2 : y - 1 ...

A: Solution is below.

Q: Let U, A, and B be defined as shown below. U ={a, b, c, d, e, f, g, h, i, j } A = { c, d, e, g, i} B...

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Q: If the utility depends only on the consumption of x and u (x) = ( 2a¯i + 3) (-4xi +2), is Marginal U...

A: Given u(x) = 2x-12 + 3-4x14 + 2

Q: Finch eign Valucs and eiguvecmo for the salloes or the ollawi

A: Given A = 344-3

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1+ i).

A: The problem is regarding complex analysis. We have to reduce the given trigonometric into real and i...

Q: Find the maximum and minimum volumes of a rectangular box whose, surface area is 1300 cm² and whose ...

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Q: Topic: Complex numbers Instruction: Perform the indicated operations. Express results in rectangular...

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Q: Solve + 3y + 2 ,: y dx = x, given y (0) = 1. dx

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Q: (A v B) -> ~C CvD ~В -> А А -> D

A: Rules of Inference

Q: II. Determine whether or not the following sets of vectors {u , v , w} are both orthogonal and ortho...

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Q: I. For the given vectors i and v , find the value of u · v and normalize = (3,–1,9, –10) 2. й 3D (3,...

A: 1. Given u→ = (2, 7, -1, 20)v→ = (3, -1, 9, -10)Sou→.v→ = (2, 7, -1, 20)·(3, -1, 9, -10)        = 6 ...

Q: Find dw/dt given = 5 cos(xy) – sin xz, x = = 1/t, y = t and z = t³.

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Q: Solution by Gauss seidel method. - 9х1 + 2х2 + Зx; 3D 7 X1 + 12x2 + 9x3 = 2 4x1 + 6х2 + 14х; 3D 1

A: Let x1 = a, x2 = b and x3 = c So Given equations are9a + 2b + 3c = 7a + 12b + 9c = 24a + 6b + 14c = ...

Q: Let A = {x x = 12k for some k E Z} Let B = { x | x = 4k for some k EZ} Prove that A CB.

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Q: This is one question but I couldn't fit the whole question in one photo so I attached two photos, th...

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Q: #1. Use mathematical induction I to prove that for all integers n 2 3, 2·3 + 3 · 4 +. + (n – 1) · n ...

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Q: 3 -2 -45 -5-

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Q: Find the general solution of the DE x(y? + x)dy - y(y?- x²)dx% = 0. %3D (x-y) In x +y In y =cx + y O...

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Q: Locate the centroid of the solid generated by the area bounded by 2x+y=D2, ×3D0, y%3D0 about x-0. O ...

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Q: SECTION 2.3 EXERCISES 1. For each of the following, compute (i) det(A), (ii) adj A, and (iii) A-1: 2...

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Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

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Q: Evaluate tne below exprassion using De Moivres meorem-

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Q: Jeremy's bedroom has two doors leading into the hallway. His house has four doors leading to the out...

A: The numbers used for the counting are called natural numbers. In this case, the number of doors of J...

Q: Show that the general solution of the equation 4,32.xy°u, = 0 is given by where f is an arbitrary fu...

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Q: +If z = 4el3, determine In z (a) in Cartesian form, and (b) in polar form Į Determine in polar form ...

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Q: 11. х2 + у? - 6х + 16у + 24 %3D 0 12. Зx2 + Зу? -42у -153%3D0

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Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for t...

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Q: the picture gives the equation, please answer the following two questions i typed below in a digital...

A: Given-  Maximize: P = 12x1 + 10x2subject to:5x1 + 3x2 ≤ 15x1 + x2 ≤ 4x1 ≥ 0, x2 ≥ 0 To find-  d) Is ...