Let T : Rn -> Rm be a onto linear transformation. Select all the true statements

Question

Let T : Rn -> Rm be a onto linear transformation. Select all the true statements from the following list. (Incorrect choices will earn you negative points) For any y in Rm there exists a unique x in Rn such that T(x) = y
For any y in Rm there is at most one x in Rn such that T(x) = y
The range of T is the entire Rm For any y in Rm there is at least one x in Rn such that T(x) = y T2, which is T composed with itself (i.e., T2(x) = T(T(x)) ) is also an onto linear transformation. T has an inverse. T must be one-to-one The equation T(x) = y in x (i.e., Let T : Rn -> Rm be a onto linear transformation. Select all the true statements from the following list. (Incorrect choices will earn you negative points) For any y in Rm there exists a unique x in Rn such that T(x) = y
For any y in Rm there is at most one x in Rn such that T(x) = y
The range of T is the entire Rm For any y in Rm there is at least one x in Rn such that T(x) = y T2, which is T composed with itself (i.e., T2(x) = T(T(x)) ) is also an onto linear transformation. T has an inverse. T must be one-to-one The equation T(x) = y in x (i.e., Let T : Rn -> Rm be a onto linear transformation. Select all the true statements from the following list. (Incorrect choices will earn you negative points) For any y in Rm there exists a unique x in Rn such that T(x) = y
For any y in Rm there is at most one x in Rn such that T(x) = y
The range of T is the entire Rm For any y in Rm there is at least one x in Rn such that T(x) = y T2, which is T composed with itself (i.e., T2(x) = T(T(x)) ) is also an onto linear transformation. T has an inverse. T must be one-to-one The equation T(x) = y in x (i.e.,

Explanation / Answer

For any y in Rm, there exists a unique x in Rn such that T(x) = y. False as T is not stated to be one-to-one.                                                For any y in Rm there is at most one x in Rn such that T(x) = y. False as T is not stated to be one-to-one.                   The range of T is the entire Rm. True, as T is onto.              For any y in Rm there is at least one x in Rn such that T(x) = y. True, as T is onto. T2, which is T composed with itself (i.e., T2(x) = T(T(x)) ) is also an onto linear transformation. False. T2 is not even defined as Rn? Rm.                           T has an inverse. False, as T is not stated to be one-to-one.         T must be one-to-one. False as not every onto linear transformation is one-to-one.                        The equation T(x) = y in x (i.e., INCOMPLETE

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