Let T be the linear transformation whose standard matrix is given. Decide if T i
ID: 3404970 • Letter: L
Question
Let T be the linear transformation whose standard matrix is given. Decide if T is a one-to-one mapping. Justify your answer. Choose the correct answer below. The transformation T is not one-to-one because the equation T(x) = 0 has only the trivial solution. The transformation T is not one-to-one because the equation T(x) = 0 has a nontrivial solution. The transformation T is one-to-one because the equation T(x) = 0 has a nontrivial solution. The transformation T is one-to-one because the equation T(x) = 0 has only the trivial solution.Explanation / Answer
Answer :
The transformation T is one to one because the equation T(x) = 0 has only trivial solution
Explanation : Let A be the standard matrix of T . Then T is one to one if and only if the equation Ax = b has atmost one solution for each b .
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