(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have attached the question. Translated: Suppose T: R^4 -> R^4 is the image so that: ......

2. Relevant equations

So I did this question and my final answers were correct: 1. not surjective 2. not injective. My method of solving this question is completely different than the answerbook thoug. Is my method correct too?

3. The attempt at a solution

1. If i put the transformation inside a matrix the result would be:

0 1 1 0--------------------------------------0 1 0 1

0 0 3 1 which can be reduced t----0 0 1 -1

0 -1 0 0-------------------------------------- 0 0 0 1

0 -1 0 1--------------------------------------- 0 0 0 0

1. learned that a condition for a surjective transformation is that there has to be a pivot position in each row, which is not true: pivot positions are in row 1, 2 and 3, but not 4. So not Surjective.

2. Secondly I learned that a condition for a injective transformation is that there can be no free variables. In the matrix above, there is one column with only zeros. This means that X1 is a free variable, it doesn't matter what value you give to it, it will not affect the final outcome.

Is what i did correct? Thanks in advance.

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# Homework Help: How to check if a transformation is surjective and injective

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