please solve all parts (1,4, 2), и2points in the xyz-space, and S7. Let ui =(0, 3, 1), из(1,1, 1), ид —{и, из, из, ид}.(1, 3, –3) represent four(i)in S.Show that we cannot find a plane that contains all the four pointsFind a linear system with 2 equations that represent two planes(ii)U and V such that u1 lies on U and u2 lies on V, and u3, U4 are solutionsof the system.:::111Find the equation of a plane P that contains three points in Ssuch that P is a subspace of R³.(iv)points in R³ such that the three points lie on a plane that corresponds toa subspace of R°. Justify your answer.Write down a necessary and sufficient condition on any three

Since part (i) is very lengthy, we solve first part only. For other part please resubmit.

Answered: 7. Let ui (1,4, 2), из (0, 3, 1), из —…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 13AEXP

See similar textbooks

Similar questions

Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.
Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z and it contains the points (1,1,1), (1,2,2), (2,-1,-2), and (3,-2,3). Set up a system of linear equations and use row reduction to determine the coefficients for this equation.
Find an equation of the plane passing through P = (1, 2, 3), Q = (0, 0, 3),and R = (−2, 5, 4).
From the system x' = -x + 5y og y' = -y show that the vector function (top of picture) is a solution of the system only if (bottom of picture) is true.
Find an equation for the plane through P(1,4,4) that contains the line of intersection of the planes 3x-y+3z=-1 and -4x+2y-4z=2
Find a plane containing the line r(t) =< 5, -4,7 > +t < 5, 5, 3 > and orthogonal to the plane 8x +2y-3z=-3
Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].
When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . , un, v} is linearly dependent, prove that v is a linear combination of the ui’s.
Find the point at which the line r(t) = <7, -7, -5> + t<5, -1, 4> intersects the yz plane.
Find a plane containing the line ¯r(t)=<−7,3,5>+t<4,8,−8> and orthogonal to the plane 5x−6y−7z=−5
Determine α so that the lines r X = (1,0,2) + λ (2, 1, 3) and s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

SEE MORE TEXTBOOKS

7. Let ui (1,4, 2), из (0, 3, 1), из — (1,1, 1), ид — (1, 3, —3) represent four 6. points in the xyz-space, and S = {u1, u2, U3, U4}. (i) in S. Show that we cannot find a plane that contains all the four points