Linear map equation and its solution

Let T:Rn→Rn be the one-to-one onto linear transformation and let T(X)=b, b∈Rn, be a linear map equation. Then it has
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Let T:R3→R2 be the linear transformation defined by T(x, y, z)=(x, y+z), where x, y, z∈R. Consider the linear map equation T(X)=b, where b=(1, 0). Then
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Let T:R2→R3 be the linear transformation defined by T(x, y)=(x, x+y, x-y), where x, y∈R. Consider the linear map equation T(X)=b, where b=(1, 0, 0). Then
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Let T:R2→R2 be the linear transformation defined by T(x, y)=(3x, 4x), where x, y∈R and let b=(3, 4). Then which of following is a solution of the linear map equation T(X)=b
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Let T:R2→R2 be the linear transformation defined by T(x, y)=(y, 0), where x, y∈R. Let the statements A and B be as given below: A: The linear map equation T(X)=(1, 4) is consistent. B: The linear map equation T(X)=(4, 0) is consistent. Then which of following holds
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