True or false question Don't need steps just true or false 1. There is only one scalar equation for a given line in 3-space.2. A line in 3-space can be represented by using a scalar equation, a vector equation,parametric equations.3. Three collinear points in space will define a plane.4. [0,2,1] +t[2,1,1] is parallel to the plane 2x+y+z=05. If the normal vectors of three planes in 3-space are coplanar then there is no solution tothe system

In this question we have to state True or False. Note: As per our policy we can answer only first…

Answered: 1. There is only one scalar equation…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 1AEXP

See similar textbooks

Similar questions

Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.
Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
write the equation of the plane with normal vector n passing through the given point in the scalar form ax + by + cz = d. n = (2, −4, 1), 1/3 , 2/3 , 1
Find the scalar equation for the plane passing through the point P=(−4, 2, 10) and containing the line L defined byx = −8+14ty = 6+4tz = 12
1. Determine the scalar equation of a plane with normal vector n = [3,1,3] that has a y-intercept of 5.
Let L be the line through the point Q=(−3, 3, −2) and direction vector d=[4, 5, 1]T. Find scalar equations of two perpendicular planes P1 and P2 intersecting in L.
Find the scalar equation of the plane r = [-2,2,7] + s[3,-2,1] + t[-2,1,5]
The equation ax + by + cz = 0 represents a plane through the origin in R3. Show that the vector n2 = (a, b, c) formed from the coefficients of the equation is orthogonal to the plane, that is, orthogonal to every vector that lies in the plane.

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

1. There is only one scalar equation for a given line in 3-space. 2. A line in 3-space can be represented by using a scalar equation, a vector equation, parametric equations. 3. Three collinear points in space will define a plane.