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I need serious help on why I am getting the answer wrong here. I followed the exact same method as: Express the following invertible matrix A as a product of elementary matrices

But the computer is telling me I am wrong.

Computer's answer: enter image description here

My answer: enter image description here

Community
  • 1
K.Wong
  • 11

2 Answers2

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The third matrix is not an elementary matrix (heck, it has a column of zeros and isn't invertible).

Batman
  • 19,390
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You left a $1$ off of $E_3^{-1}$. It should be $$\pmatrix{1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & \color{red}1}$$

Once you make that change you should get the correct solution.

For future reference, you should note that the comment that the computer gives you was big hint about your mistake. It says that at least one of your matrices isn't an elementary matrix. So you should have gone back through, saw that the matrix you have for $E_3^{-1}$ isn't an elementary matrix, and then reworked that one.