SOLUTION: A is nxn matrix such that A^2=I and B is nx1 real vector then Ax=B has_______ option are:1) no solution 2)unique solution 3)infinitely many solution 4) none

Algebra ->  Matrices-and-determiminant -> SOLUTION: A is nxn matrix such that A^2=I and B is nx1 real vector then Ax=B has_______ option are:1) no solution 2)unique solution 3)infinitely many solution 4) none       Log On


   

Question 1137870: A is nxn matrix such that A^2=I and B is nx1 real vector then Ax=B has_______
option are:1) no solution 2)unique solution 3)infinitely many solution
4) none
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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Under given condition, the matrix A has a non-zero determinant.   (Actually, its determinant is +/- 1.)


Therefore, the matrix A is non-degenerated.


Hence, any equation of the given form with the given coefficient matrix has a unique solution.


Answer option 2).

Solved, answered and explained.

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