a) Verify that the sum of two bilinear forms is a bilinear form. b) Verify that the product of a scalar and a bilinear form is a bilinear form.

Q: Find the scalar equation of the plane that contains these points: A (1, 13, 2), B (-2, -6, 5) and C…

A: In this question, we want to find the scalar equation of a plane Passing through given three points.

Q: Describe the set of points in the complex plane satisfies Z? + Z2

A: Introduction: The sum of a real and an imaginary number is a complex number. A complex number is…

Q: Which are the foci of the hyperbola represented by 5y² - 4x² - 80 = 0? O(-8,0) and (6.0) O (0,8) and…

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Q: 15. x2 - 8x + 2y + 10 = 0

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Q: A plane in 3D-space system A. is generated by at least three points. B. can lie in more than one…

A: A plane in 3D-space system is generated by three points from which if the first nd second points…

Q: e diagonalizable?

A:

Q: Determine the vertical traces of elliptic and parabolic cylinders in standard form.

A: Firstly the trace of a surface which is actually a cross section or the curves of intersection of a…

Q: If you project a square onto a plane, what shape do you get?

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Q: 8. Determine the dot product of u = [7,-4.1] and v = [3.-2.2].

A: Dot product is also known as the scalar product.

Q: If possible, find scalars c1 and c2 so that

A: Given: c11-2+c23-4=-56 c11-2=c1-2c1 c23-4=3c2-4c2 Therefore, c1-2c1+3c2-4c2=-56…

Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

Q: Find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy +…

A: To find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy…

Q: (b) Determine a cycle decomposition of a hypercube Q4-

A: Here, we need to determine a cycle decomposition of a hypercube Q4

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

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

Q: Determine whether the statement" The weight of a car is a scalar", is true or false. If it is false,…

A: Scalar: Many quantities in geometry and physics, such as volume, mass, temperature and time can be…

Q: In each part, name the conic section described. (a) The set of points whose distance to the point…

A: To Determine:  In each part, name the conic section described.(a) The set of points whose distance…

Q: 4. Describe how you can tell from the scalar equations if two planes are a) parallel and distinct or…

A: a) Given that, two planes are parallel, distinct or coincident. The general form of an equation of a…

Q: Define the dot product (scalar product) of two vectors. Which al-gebraic laws are satisfied by dot…

A: Let (a1,a2,a3,....) and (b1,b2,b3,...) are two vectors. Then the dot product is defined by:

Q: Which figure represents a three-dimensional solid with only one face?

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Q: A triangle is inscribed in a rectangular hyperbola such that the tangent at one of the vertices is…

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Q: Determine whether the statement " Two planes in space are either intersecting or parallel ", is true…

A: The given statement is ''Two planes in space are either intersecting or parallel''.

Q: Q, : Describe the set of points in the complex plane that satisfy z +1| (2) - = 2 z -1 11-1 =1리 (1)

A: Given that  1)z=z-i2)z+1z-1=2 Find out the set of points

Q: State whether the equation 25x2 - 16y + 16z2 = 1 defines (enter number of statement): 1. A…

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Q: Exercise 1 - Show that 1 1 3 span -2 R. %3D 3 -4

A: The set pf vectors: 123,12-4,3-21  To show: Three vectors span R3.

Q: Identify and sketch the following conic 4x2 - y2 = 16

A: The solution is:

Q: Determine the length of the latus rectum of the following conic section: 16z + 9y? - 64.x- 54y+1 0 O…

A: 16x2+9y2-64x-54y+1=016x2-64x+9y2-54y=-116(x2-4x)+9(y2-6y)=-116(x2-4x+4)+9(y2-6y+9)=-1+64+8116(x-2)2+…

Q: Give an example of the reflective property of a parabola.

A: Given:The parabola is the set of points in the plane that are equidistant from a fixed line, (the…

Q: Find the surface of the regular pyramid.

A:

Q: 2. Draw a figure to illustrate part of the infinite pattern that can be derived from a given…

A: Given data is: Draw a figure to illustrate the part of infinite pattern that can derived from…

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 5. Draw/Describe the set of points in the complex plane that satisfies |z - il < 2.

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Q: Find an equivalent quadratic form by using a diagonal rotation, (by the principle axis theorem. I…

A: Given: Q=2x2+4y2+6yz-4z2=80

Q: Describe the set of points in the complex plane that satisfy z + (2)- |1– |

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Q: Show that the complex numbers 2 + 3i and 1 – 2i generate the vector space

A: Given complex numbers are z1=2+3i    and    z2 =1-2i and   given vector space  is   ℂ over ℝ

Q: Find the dimentions of the largest rectangle that can be inscribed in the ellipse x^2+5y^2=25 A.…

A:

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: find the vertices and foci of the conic section.

A:

Q: The triangle has vertices A(-2,3), B(0,0), and C(-1,-1). Plot the coordinates of the supermen logo…

A:

Q: Given that complex u and v,  prove that: ||u| - |v|| ≤ |u - v |

A: In the given question we have to prove that                     for two complex number u and v…

Q: Determine the length of the latus rectum and distance between the foci of the conic section: 16x^2…

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Q: Compute the order of each element in the Quaternions, Q8. Show your work.

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Q: If they are linearly dependent, find scalars that are not all zero such that the equation below is…

A: Given  -4-3-33,-1-430,-3104 and -2-8-6-2

Q: Sketch the following Cartesian products on an x, y-plane. (2) {2, 4, 6} × {0, 1, 2} (b) [0, 2) x {1,…

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Q: 9. The triple scalar product is given by (u x v) w = E,",V,W Expand this equation X V and simplify,…

A: Let u=(u1 , u2 , u3 ) and v=(v1 , v2 , v3 ) and solve it.

Q: . Find the vertices of the hyperbola. 16x2 - 9y? = 144 %3D (0, O (0, - 3) and (0, 3) O (0, - 4) and…

A: This question is related to hyperbola, We will solve it using given information.

Q: An example of 4-dimensional hypercube Q 4

A: Given: Let's determine the example of the 4-dimensional hypercube.

Q: Write a MATLAB code to find the equations of the tangent lines of the ellipse x2 + 4y2 = 36 that…

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Q: Find the centroic

A: Centroid of semi circle is given as 4r3π Here radius of bigger circle is 9 and that of smaller…