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
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
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
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
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