CODEWITHSUNDEEP
rlinear-equation
Trigger
Trigger

Reputation: 35

Linear Equation not possible to solve?

I want to solve a linear equation A*x=b with

A<-matrix(c(1,4,9,5,2,3,8,4,3,2,7,3,4,1,6,2),4,4)
b<-c(2,0,7,9)

If I then use the solve() function it shows an error:

solve(A,b)
Error in solve.default(A, b) : 
  system is computationally singular: reciprocal condition number = 1.06241e-18

Is there any fault in my approach or is this linear equation not possible to solve?

Upvotes: 0

Views: 58

Answers (1)

St&#233;phane Laurent
St&#233;phane Laurent

Reputation: 84529

There are some linear relationships between the columns of A:

> A <- matrix(c(1,4,9,5,2,3,8,4,3,2,7,3,4,1,6,2),4,4)
> # linear relationship between columnds 2,4,3:
> A[,2] + A[,4]
[1]  6  4 14  6
> 2 * A[,3]
[1]  6  4 14  6
> # linear relationship between columnds 1,3,2:
> A[,1] + A[,3]
[1]  4  6 16  8
> 2 * A[,2]
[1]  4  6 16  8

Therefore, A is not invertible.

Upvotes: 1

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