SOLUTION: Let A be a nonsingular matrix. If the set {X1,X2,X3} is linearly independent, then the set {AX1,AX2,AX3} is also linearly independent
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Question 1026822: Let A be a nonsingular matrix. If the set {X1,X2,X3} is linearly independent, then the set {AX1,AX2,AX3} is also linearly independent Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! { ,,} a linearly independent set means that the equation
,
will be true only if , , are all equal to 0.
(The 0 on the right side is the zero column vector.)
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In view of the fact that (i) there is no possibility for any of the vectors to become zero vectors or to be linear combinations of the other vectors because A is nonsingular, and (ii) the only possible values for the c constants are still 0, we conclude that { ,,} is still a linearly independent set.
