The solution space for this system is a subspace of R³ and so must be a line through the origin, a plane through the origin, all of R³, or the origin only. For the given system, determine which is the case. If the subspace is a plane, find an equation for it, and if it is a line, fir parametric equations. x+3y+6z= 0 2x+4y+4z=0 4x+y-3z = 0

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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Author:HOUGHTON MIFFLIN HARCOURT
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Chapter5: Solving Systems Of Linear Equations
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The solution space for this system is a subspace of R3 and so must be a line through the origin, a plane through the origin, all of R³, or
the origin only. For the given system, determine which is the case. If the subspace is a plane, find an equation for it, and if it is a line, find
parametric equations.
x + 3y+6z= 0
2x+4y+4z = 0
4x + y - 3z = 0
O The solution space is all of R³.
O The solution space is the line x-t, y=t,z=0.
O The solution space is the line x=3t, y = - 6t, z=0.
O The solution space is the plane x + 3y+z = 0.
○ The solution space is the origin only.
O The solution space is the plane x + 3y+6z=0.
Transcribed Image Text:The solution space for this system is a subspace of R3 and so must be a line through the origin, a plane through the origin, all of R³, or the origin only. For the given system, determine which is the case. If the subspace is a plane, find an equation for it, and if it is a line, find parametric equations. x + 3y+6z= 0 2x+4y+4z = 0 4x + y - 3z = 0 O The solution space is all of R³. O The solution space is the line x-t, y=t,z=0. O The solution space is the line x=3t, y = - 6t, z=0. O The solution space is the plane x + 3y+z = 0. ○ The solution space is the origin only. O The solution space is the plane x + 3y+6z=0.
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