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linear algebra A' is A when two of A lines switched,A Invertible prove (A+A')x=0...
A is a n*n matrix
A' is the matrix A when two two lines i,j are switched.
(switch two random lines is A and you get A')
If A Invertible Prove that the system (A+A')x=0 has infinite solutions
linear algebra including Determinant
Well I know that A+A' has two identical lines so when subtracting them I get a line of 0 and then Because I know there is a line of 0 I know that there are infinite solutions...
But I did not used the fact that A is Invertible...
How do I solve it while using this fact? , I try to use Determinant but I do not mange to.
Thank you.
Homework Statement
A is a n*n matrix
A' is the matrix A when two two lines i,j are switched.
(switch two random lines is A and you get A')
If A Invertible Prove that the system (A+A')x=0 has infinite solutions
Homework Equations
linear algebra including Determinant
The Attempt at a Solution
Well I know that A+A' has two identical lines so when subtracting them I get a line of 0 and then Because I know there is a line of 0 I know that there are infinite solutions...
But I did not used the fact that A is Invertible...
How do I solve it while using this fact? , I try to use Determinant but I do not mange to.
Thank you.