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[M] In Exercises, let T be the linear transformation whose
Chapter 1, Problem 37E(choose chapter or problem)
QUESTION:
PROBLEM 37E
[M] In Exercises, let T be the linear transformation whose standard matrix is given. In Exercises, decide if T is a one-to-one mapping. In Exercises, decide if T maps ℝ5 onto ℝ5. Justify your answers.
Questions & Answers
QUESTION:
PROBLEM 37E
[M] In Exercises, let T be the linear transformation whose standard matrix is given. In Exercises, decide if T is a one-to-one mapping. In Exercises, decide if T maps ℝ5 onto ℝ5. Justify your answers.
ANSWER:
Solution
Step 1
In this problem we have to determine whether T is a one-to-one mapping or not.
We know that “Let be a linear transformation. Then T is one-one if and only if the equation T(x)=0 has only the trivial solution”. ….. (1)
Given
