1. (5pts) Solve the following system I1 + 2x2 – 13 + 3r4 2x1 + 4r2 – 2x3 + 7x4 = 10 -11+2x2 + x3 – 4x4 = 4 -6 %3D Write the solution set in parametric vector form.

Q: Solve cach system using Cramer's Rule. 5r – 5y = 7 (a) 2r – 3y = 6 2r + 3y + 2z = -2 -1- 3y – 8z =-2…

A: a) 5x- 5y=72x-3y=6b)2x+3y+2z=-2-x-3y-8z=-2-3x+2y-7z=2

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: Find a system of two equations in two variables, x1 and x2, that has the solution set given by the…

A:

Q: Give the parametric vector form of the general solution of the following system of linear equations:…

A:

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

A:

Q: 1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k…

A: Here the given matrices are                                      A=abcd and B=dcba We have to show…

Q: The scalar equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is: 2x + 5y…

A: Put the points one by one on the given planes and check satisfied or not

Q: Consider the system of equations below = 0 X1 – 2x1 – x3 + 3x4 -2x1 + 4x2 + 5x3 - 5x4 3x1 – 6x2 –…

A: Topic : Linear algebra  As per our guidelines, At a time only one question will be answered.

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

A:

Q: Find a parametric representation of the solution set of the linear equation.2x − 4y = 0

A: To find the parametric representation of the solution set, solve the given equation for the value of…

Q: Use Cramer's Rule to solve the system.

A: 0.4x+1.2y=0.41.2x+1.6y=3.2

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: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: 1. Verify whether the vector X is a solution of the given system where 2. X' = X; X=

A:

Q: 1. Verify whether the vector X is a solution of the given system where X; X =| 3 X' =

A: Given:

Q: Solve the following system T1 + 2x2 – 13 + 3x4 2.x1 + 4x2 – 2z + 7x4 4 10 -x1 + 2x2 + x3 – 4r4 -6…

A: We have solve given system of linear equations-

Q: I can't find a way to solve this practice problem. Can you work it out so I can see how it's done?…

A:

Q: x1 x₁ + 3x25x3 = 4 x₁ + 4x2 - 8x3 = 7 -3x17x2 + 9x3 = -6

A: We have the set of linear equations as x1+3x2-5x3=4x1+4x2-8x3=7-3x1-7x2+9x3=-6

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: Use Cramer's Rule to solve the system.

A: If we have linear system, a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3 So using Cramer's rule, x=DxD,…

Q: 2 The equation of the plane passing through the origin and containing the vectors -1 and has…

A:

Q: Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and…

A:

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

A:

Q: Give the parametric vector form of the general solution of the following system of equations: -1…

A: x1-5x2-2x3      -4x5-4x6  =-1                   -x4+4x5-3x6  =     8x1-5x2               -6x5 -6x5=…

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: 1. Verify whether the vector X is a solution of the given system where 2. X'= X; X = e'+ %3D

A:

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

A:

Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: Solve the following system. (Enter your answers as a comma-separated list. If there are infinitely…

A: Let us add the equations

Q: 1. Consider the following system of linear equations: X1 + kx2 = 2 kæ1 + x2 + 13 = 1 x1 + x2 + x3 =…

A:

Q: Solve for the system of linear equation using Cramer's Rule x + y – z = 0 2x – 3y + z = 1 2x + y +…

A:

Q: Consider the following system: 2х + 3у — 2х х — 2у + 32 - 2y + 4z 1 1 %3D 2x – 2 (a) Find the…

A: The given equations are 2x + 3y - 2z = 1 x - 2y + 3z = -1 2x - 2y + 4z = -2 to find the parametric…

Q: Consider the system Sai = 2x2 |a = -2.01 Subject to the initial conditions x1(0) = 3, x2(0) = 4.…

A: Given system is x'1=2x2x'2=-2x1 With initial conditions x10=3 and x20=4

Q: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of…

A: Reduce the equation    4x^2 + y^2 + 4z^2 - 4y − 24z + 36 = 0    to one of the canonical forms of the…

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (a) Solve the system Ax = b, and write the solution in parametric vector form. (b) Using the result…

A: In this question we used the Gauss elimination method

Q: Given 2 8 -2 -10 -67 [1 4 0 -4 -17 rref 1 4 -2 -6 -5 0 0 1 1 -1 -4 1 5 3 0 0 use the reduced row…

A:

Q: Consider the following system of linear equations: 2.51c1 + 1.48x2 + 4.53x3 = 5.56 1.48x1 + 0.93.x2…

A:

Q: 1. For the system below, describe the solutions in parametric vector form: + 3x3 + 2x2 + 5x3 2.x1 +…

A: firstly make an augumented matrix then solve this matrix by Gauss -Jordan elimination method.

Q: 1. Given the system -8 -5 X' * - ( 3 5 ) * X 5 2 (a) Find the general solution. (b) Find the…

A:

Q: Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at…

A:

Q: The vector (8, 0, 1) is a solution of the linear system: X1 + 4x2 – 4x3 = 4 5х1 + 16х2 — 16х; — 24…

A: Linear equation: - Linear equations are simply another class of "equations." Linear equations will…

Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

A:

Q: Describe the solutions of the given system into parametric vector form.x1+x2+ 2x3= 9,2x1+ 4x2−3x3=…

A: Here a+b+2c=92a+4b-3c=13a+3b+6c=27Now converting given equations into matrix…

Q: Plot the following and their normal vectors. 2x-2y + 2z = 15 3x - 3y + 3z = -13 Describe the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 3. Find the equation of the plane parallel to the plane with equation 18x + 6y – 5z = 0 and passing…

A:

Q: 2. Answer and show the Solution in parametric vector form. a. x, + 3x2 - 3x3 = 7 c. x, + 2x;- 3x3 =…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.