Demuestre que la matriz $A = \begin{bmatrix} 2 & 4 & 6 \\ 4 & 5 & 6 \\ 3 & 1 & -2 \end{bmatrix}$ es invertible y escríbala como un producto de matrices elementales.
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$A = \begin{bmatrix} 2 & 4 & 6 \\ 4 & 5 & 6 \\ 3 & 1 & -2 \end{bmatrix}$ Show more…
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Let A = [0 1; -3 -24]. One can show that A is invertible and that its inverse A^-1 can be written as a product of elementary matrices: A^-1 = E3E2E1. Use this information to write A as a product of elementary matrices A = E1^-1 E2^-1 E3^-1. (You should solve this problem by performing the same process done in Problem 6 used to write A as a product of elementary matrices.) E1^-1, E2^-1, E3^-1.
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Perform the indicated row operation(s) and write the new matrix. $$\left[\begin{array}{ccc|c} -3 & 2 & 0 & 0 \\ 1 & 1 & 2 & 6 \\ 4 & 1 & -3 & 2 \end{array}\right] \begin{array}{l} \mathrm{R} 1 \leftrightarrow \mathrm{R} 2 \\ -4 \mathrm{R} 1+\mathrm{R} 3 \rightarrow \mathrm{R} 3 \end{array}$$
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