×
×

# . (a) A hyperplane in the n-dimensional Euclidean space Rn has an equation of the form

ISBN: 9781118474228 398

## Solution for problem T2 Chapter 10.1

Elementary Linear Algebra, Binder Ready Version: Applications Version | 11th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Elementary Linear Algebra, Binder Ready Version: Applications Version | 11th Edition

4 5 1 404 Reviews
21
0
Problem T2

. (a) A hyperplane in the n-dimensional Euclidean space Rn has an equation of the form a1x1 + a2x2 + a3x3 ++ anxn + an+1 = 0 where ai, i = 1, 2, 3,..., n + 1, are constants, not all zero, and xi, i = 1, 2, 3,...,n, are variables for which (x1, x2, x3,...,xn) Rn A point (x10, x20, x30,...,xn0) Rn lies on this hyperplane if a1x10 + a2x20 + a3x30 ++ anxn0 + an+1 = 0 Given that the n points(x1i, x2i, x3i,...,xni), i = 1, 2, 3,..., n, lie on this hyperplane and that they uniquely determine the equation of the hyperplane, show that the equation of the hyperplane can be written in determinant form as x1 x2 x3 xn 1 x11 x21 x31 xn1 1 x12 x22 x32 xn2 1 x13 x23 x33 xn3 1 . . . . . . . . . ... . . . . . . x1n x2n x3n xnn 1 = 0 (b) Determine the equation of the hyperplane in R9 that goes through the following nine points: (1, 2, 3, 4, 5, 6, 7, 8, 9) (2, 3, 4, 5, 6, 7, 8, 9, 1) (3, 4, 5, 6, 7, 8, 9, 1, 2) (4, 5, 6, 7, 8, 9, 1, 2, 3) (5, 6, 7, 8, 9, 1, 2, 3, 4) (6, 7, 8, 9, 1, 2, 3, 4, 5) (7, 8, 9, 1, 2, 3, 4, 5, 6) (8, 9, 1, 2, 3, 4, 5, 6, 7) (9, 1, 2, 3, 4, 5, 6, 7, 8)

Step-by-Step Solution:
Step 1 of 3

7/26/2017 OneNote Online 3.3 Monday, September 29, 2014 10:27 AM https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!2562&cid=36773184373a8f0b&app=OneNote&authkey=Avz_e_hLmB4xJLw...

Step 2 of 3

Step 3 of 3

##### ISBN: 9781118474228

This full solution covers the following key subjects: . This expansive textbook survival guide covers 80 chapters, and 2108 solutions. The full step-by-step solution to problem: T2 from chapter: 10.1 was answered by , our top Math solution expert on 03/14/18, 04:26PM. Since the solution to T2 from 10.1 chapter was answered, more than 218 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Elementary Linear Algebra, Binder Ready Version: Applications Version, edition: 11. The answer to “. (a) A hyperplane in the n-dimensional Euclidean space Rn has an equation of the form a1x1 + a2x2 + a3x3 ++ anxn + an+1 = 0 where ai, i = 1, 2, 3,..., n + 1, are constants, not all zero, and xi, i = 1, 2, 3,...,n, are variables for which (x1, x2, x3,...,xn) Rn A point (x10, x20, x30,...,xn0) Rn lies on this hyperplane if a1x10 + a2x20 + a3x30 ++ anxn0 + an+1 = 0 Given that the n points(x1i, x2i, x3i,...,xni), i = 1, 2, 3,..., n, lie on this hyperplane and that they uniquely determine the equation of the hyperplane, show that the equation of the hyperplane can be written in determinant form as x1 x2 x3 xn 1 x11 x21 x31 xn1 1 x12 x22 x32 xn2 1 x13 x23 x33 xn3 1 . . . . . . . . . ... . . . . . . x1n x2n x3n xnn 1 = 0 (b) Determine the equation of the hyperplane in R9 that goes through the following nine points: (1, 2, 3, 4, 5, 6, 7, 8, 9) (2, 3, 4, 5, 6, 7, 8, 9, 1) (3, 4, 5, 6, 7, 8, 9, 1, 2) (4, 5, 6, 7, 8, 9, 1, 2, 3) (5, 6, 7, 8, 9, 1, 2, 3, 4) (6, 7, 8, 9, 1, 2, 3, 4, 5) (7, 8, 9, 1, 2, 3, 4, 5, 6) (8, 9, 1, 2, 3, 4, 5, 6, 7) (9, 1, 2, 3, 4, 5, 6, 7, 8)” is broken down into a number of easy to follow steps, and 260 words. Elementary Linear Algebra, Binder Ready Version: Applications Version was written by and is associated to the ISBN: 9781118474228.

#### Related chapters

Unlock Textbook Solution