Vector Algebra question Watch

E--
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A = \begin{pmatrix} 1 & 0  \\-5 & 2 \end{pmatrix}

Find elementary matrices E1 and E2 such that E_1 E_2 A = I
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RDKGames
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(Original post by E--)
A = \begin{pmatrix} 1 & 0  \\-5 & 2 \end{pmatrix}

Find elementary matrices E1 and E2 such that E_1 E_2 A = I
You've used this site enough to know that you should post any thoughts / attempts first.
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E--
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(Original post by RDKGames)
You've used this site enough to know that you should post any thoughts / attempts first.
My thoughts
Elementary matrices are invertiable. And E1 and E2 must be a 2 x 2 matrices.
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RDKGames
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(Original post by E--)
My thoughts
Elementary matrices are invertiable. And E1 and E2 must be a 2 x 2 matrices.
Well, you're not wrong, but it isn't much to go on.

Notice that (E_1E_2)A = I and the only way this is possible is if the product E_1E_2 is the inverse of A. [We simply use the fact that A^{-1}A = I here]

Hence E_1 E_2 = A^{-1}. What is A^{-1} ?

If you can find two elementary matrices which multiply to give A^{-1} then you're done.
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DFranklin
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(Original post by RDKGames)
Well, you're not wrong, but it isn't much to go on.

Notice that (E_1E_2)A = I and the only way this is possible is if the product E_1E_2 is the inverse of A. [We simply use the fact that A^{-1}A = I here]

Hence E_1 E_2 = A^{-1}. What is A^{-1} ?

If you can find two elementary matrices which multiply to give A^{-1} then you're done.
I understand he hasn't given you much to go on, but I feel this is probably going to send the OP in the wrong direction; the intent of the question is clearly to use 2 elementary row operations to reduce A to the identity and then make E1,E2 the corresponding elementary matrices.
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