in Linear Algebra
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I need to calculate determinant of a 2*2 matrix such as

$\begin{bmatrix} 2 &2 \\ 4& 9 \end{bmatrix}$

I proceeded by making it a upper triangular matrix and then using the negetives of the multipliers to get the lower triangular matrix.

U was obtained by doing R2->-2R2+R1 which is equal to $\begin{bmatrix} 2 &2 \\ 0& 5 \end{bmatrix}$

When I used to negative of the multiplier ,i.e. 2 to get the lower triangular matrix,  $\begin{bmatrix} 1 &0 \\ 2& 1 \end{bmatrix}$.

But the product of L and U is not coming out to be equal to the orig matrix. What am I doing wrong ?
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1 Answer

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process is correct and even the product of L and U matrix is coming out as the original matrix. Calculate once again properly.

L and U matrix can also be founded by LU-decomposition method.

Let A=L.U

L=$\begin{bmatrix} 1&0\\ L21&1 \end{bmatrix}$

U=$\begin{bmatrix} U11&U12\\ 0&U22 \end{bmatrix}$

From here lower and upper matrix can be evaluated.

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