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

Matrix A =

0 1 0

0 0 1

12 8 -1

Let E1 = a(A)(A+2I)^{2}

Let E2 = b(A)(A-3I)

For each of these, calculate the image and the kernel

2. Relevant equations

I found a(A) to be 1/25

and b(A) to be 1/25*(A-7I)

Also, if I am not mistaken, I think KernelE1 = ImageE2 and vice versa

Matrix E1 =

4 4 1

12 12 3

36 36 9

Matrix E2 =

21 -10 1

12 29 -11

-132 -76 40

3. The attempt at a solution

Um... well if v1, v2, v3 are the column vectors of E1 respectively, and w1, w2, w3 are those of E2, isn't {w1, w2, w3}α the Kernel of E1 and Image of E2 (and the other way around)???

Part two says to find a new basis such that the linear transformation corresponding to A is represented by

-2 1 0

0 -2 0

0 0 3

Where do I even begin this one?

PS: Is there a way to add matrices on this forum? It's a little messy this way.

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# Finding Kernel and Image of Matrix transformation

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