Consider the equation: x1 + 2x2 − 3x3 − x4 = 0 a) This equation describes a ’plane’ in R4. This plane is the nullspace N(A) of what matrix A? (Write the equation as Ax = 0.) b) Find two linearly independent vectors that are in this plane. c) Now find three linearly independent vectors that are in this plane. d) Can you find four linearly independent vectors that are in this plane? Why or why not?
Consider the equation: x1 + 2x2 − 3x3 − x4 = 0 a) This equation describes a ’plane’ in R4. This plane is the nullspace N(A) of what matrix A? (Write the equation as Ax = 0.) b) Find two linearly independent vectors that are in this plane. c) Now find three linearly independent vectors that are in this plane. d) Can you find four linearly independent vectors that are in this plane? Why or why not?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the equation: x1 + 2x2 − 3x3 − x4 = 0
a) This equation describes a ’plane’ in R4. This plane is the nullspace N(A) of what matrix A? (Write the equation as Ax = 0.)
b) Find two linearly independent
c) Now find three linearly independent vectors that are in this plane.
d) Can you find four linearly independent vectors that are in this plane? Why or why not?
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