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a) How many leading ones are in the RREF of a system of ten equations in ten variables having a solution set that is a plane in R10? Explain. b) How many leading ones are in the RREF of a system of ve equations in four variables having a solution set that is a point in R4? Explain.

a) How many leading ones are in the RREF of a system of ten equations in ten variables having a solution set that is a plane in R10? Explain. b) How many leading ones are in the RREF of a system of ve equations in four variables having a solution set that is a point in R4? Explain.

Advanced Engineering Mathematics
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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a) How many leading ones are in the RREF of a system of ten equations
in ten variables having a solution set that is a plane in R10? Explain.

b) How many leading ones are in the RREF of a system of ve equations
in four variables having a solution set that is a point in R4? Explain.

Expert Solution
Step 1

(a)  Answer : 8 

  Explanation :  Number of variables - number of leading ones = number of parameters

                       ⇒   10 - 8  =  2

So every vector in R10 is a linear combination of two independent vectors. Thus the solution set is a plane in R10.

Note  :   If Leading ones are 9 then we got number of parameters = 1, the solution set is a line.

 

 

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