1. The equation of the sphere x2 + y²+z² + 2ux + 2vy + 2wz + d = 0 passing through the points (0,0, 0), (0,1,–1), (-1, 2, 0), (1, 2,3) reduces to the simultaneous linear equations given by v- w +1= 0,u + 2v + 3w = -7,-2u + 4v + 5 = 0 Find the unknowns u, v and w using Matrix inverse method.

Q: Identify the graph of the linear equation 4x + 2y + z = 8 in three dimensional space. (0,0,2) (0,…

A: We need to identify the graph of the function 4x+2y+z=8 We will do so by seeing if the points that…

Q: Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the…

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Q: 5. Find the equation of the plane containing the points P(3, 2, 1), Q(2, 1, -1), and R(-1, 3, 2)

A: Let position vectors of point P(3,2,1) , Q(2,1,-1), and R(-1,3,2) are a→,b→ and c→

Q: 2. the lines y and y = 4- and whose lies in the plane z + y Solution: v-4-2 dr V2 - sphp(li + a)…

A: Integration

Q: Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9.…

A: As per guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

Q: The diagram approximately Illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 3x+3y+3z+1=0…

A: Given planes are,    x + y + z + 1 = 0  2x + 2y + 2z + 1 = 0  3x + 3y + 3z + 1 = 0    Thus, normals…

Q: In Exercises 1–3, give a geometric description of the set of points in space whose coordinates…

A: Hi there! Thank you for the question, but as per our guidelines we can solve only one question at a…

Q: 19. 19. Find an equation of the plane that passes through the points (3.0. 1). (2. 2.3). (7,1, 4). 점…

A: The plane is passing through the points (3, 0,-1) , (-2, -2, 3) and (7, 1, -4)

Q: Prove that the system of parabola y2= 4a(x+a) is self orthogonal

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Q: Consider the following nonhomogeneous linear system: xi = 2x1 – x2 + t? - x2 = 3x1 – 2x2 + t | 2.…

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Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

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Q: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

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Q: prove that the system of parabolas y2=4a(x+a) is self orthogonal

A: We show that the family contain both members with slope m and slope -1/m. Hence the family will be…

Q: (24 17. 3417.4) %3D Find the equation of the plane that contains the line x = 3t, y = 6 - t, z = 4…

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Q: The equation of the plane passing through A(2,1,-1), B(0,-2,0), and C(1,-1,2) is: None of these…

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Q: Determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4,9, -3) and R(3,…

A: To determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4, 9, -3), and…

Q: The equation of the plane passing through A(2,1, – 1), B (0, –2,0), and C(1,-1,2) is: O 2x+y-z=0…

A: solve the following

Q: If the plane through the points P(1, 1, -1), Q(3,0, 2), and R(-2,1,0), which of the following are…

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Q: Show that the system of confocal and co-axial parabolas y²-4a(a+x) is self orthogonal, where a is…

A: If the two curves in the family cut each other at the right angle, then they are considered as self…

Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1, 2), C =…

A: The given points are A=(-1,0,2), B=(2,-1,2), C=(3,-3,-3).

Q: prove that the system of parabolas y² = 4a(x + a) is self orthogonal

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Q: In Exercises 15–16, each linear system has infinitely many so- lutions. Use parametric equations to…

A: a) From the second equation we get: 6x-9y=33(2x-3y)=32x-3y=1 So both equations are same. From any…

Q: Find a parametric representation of the solution set of the linear equation.−3x + 4y − 2z = 1

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Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1,2), C =…

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Q: 2. Show that ( 1, 6), (0, 3), (1, 2), and (2, 3) lie on a common parabola.Hint: For scratch work,…

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Q: To study the changes in boundary temperatures on a steel plate, lets assume that T1, 72. T3, T4 be…

A: Since, Temperature at each point is the average of the four nearest points. Thus,…

Q: 17) An equation of a plane passing through the point ( 1, -2, 3) and containing the line L: x = 3 –…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1=0 3x+3y+3z+1=0…

A: True

Q: The equation of the plane passing through A(2,1,-1), B (0,-2,0), and C(1,-1,2) is: None of these O…

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Q: Consider the following nonhomogeneous linear system: Y = Y2 + e* Y2 = Y1 – 3e3t - 2.Using MUC, which…

A: Method of Undetermined Coefficient::

Q: Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation: | x…

A: Solution..

Q: Find the point on the curve of intersection of the paraboloid x² • y² + 2z=4 and the plane x-y+ 2z…

A: This question can be solved by options because we have only two equations and three variables.

Q: Find the vertex of the paraboloid z=x2+4y2−xy+6x−5y+1

A: The paraboloid is of two type, one is elliptic and another is hyperbolic ,  By suitable choice of…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

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Q: A- Find the distance between the line (y =x+3) and center of circle (x+y-2x-0). B- Using Cramer's…

A: (A) Given,      equation of a line y=x+3 and center of circle x2+y2-2x=0      To Find: Distance…

Q: Find the equation of the plane passing through the three points A = (-1,0,2), B= (2, –1,2), C = (3,…

A: Given problem:- Find the equation of the plane passing through the three points A = (- 1, 0, 2) B =…

Q: 8. Check if the two lines given below are coplanar or not: x = 1+t, y =1+2t, z = 3 +t and a = 3 + s,…

A: We have to check weather the given lines are coplaner are not.

Q: 11. In each part, solve the linear system, if possible, and use the result to determine whether the…

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Q: Consider the following system of linear equations 31 + 2y + z = 0 I + y + 2 = 0 2 = 0 with solutions…

A: The given system of equations are non-homogenius type(AX=0).

Q: Let Ax = b be the system 7x +y+z+w= – 13 3x +6y – z +w= -5 5x +4y - 7z +9w= - 1 find the solution by…

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Q: The equation of the plane passing through A(2,1,-1), B(0,–2,0), and C(1,-1,2) is: None of these O…

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Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: 20. The Cartesian equation of the plane which contains the point (1, -2, 3) and perpendicular to x-7…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Make a sketch in the xy-plane in order to determine the number of solutions to the given linear…

A: Given:- x + 4y = 8 3x + y = 3 To find:- Make a sketch in the xy-plane in order to determine the…

Q: In three dimensional space, the equation |1+2x+3x2 2+3x +x2 3+x+ 2x2 1+2y +3y 2+3y+y² 3+y+ 2y² = 0,…

A: In three dimensional space ,the given equation represent

Q: What is the symmetric equation of the line through the points (2,1,1) and (5,-1,2). O a.…

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Q: A system of particles are located on the x-axis with masses (in kg) 7, 12, 2, 10, and 3 whose…

A: We have, a system of particles are located on the x-axis with masses (in kg) 7, 12, 2, 10, and 3…

Q: Find the equation of the plane passing through the point P(1,-1,2) and parallel to the lines =Dz and…

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Q: 8. Check if the two lines given below are coplanar or not: x = 1+t,y =1+ 2t, z = 3+t and x = 3+ s, y…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.