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## Main Question or Discussion Point

X ={(x1,x2,x2 −x1,3x2):x1,x2 ∈R}

f(x1,x2,x2 −x1,3x2)=(x1,x1,0,3x1)

1. Find a basis for X.

2. Find dim X.

3. Find ker f and im f

4. Find bases for ker f and im f

5. Is f a bijection? Why?

6. Find a diagonal matrix for f.

My attempt:

1. (1, 1, 0, 3) and (1, 2, 1, 6)

2. Dim X = 2

3. Ker f = 0, im f = X

4. (0,0,0,0)

5. I guess no, but do not know how to explain

6. No idea

f(x1,x2,x2 −x1,3x2)=(x1,x1,0,3x1)

1. Find a basis for X.

2. Find dim X.

3. Find ker f and im f

4. Find bases for ker f and im f

5. Is f a bijection? Why?

6. Find a diagonal matrix for f.

My attempt:

1. (1, 1, 0, 3) and (1, 2, 1, 6)

2. Dim X = 2

3. Ker f = 0, im f = X

4. (0,0,0,0)

5. I guess no, but do not know how to explain

6. No idea