Determinant using gaussian elimination

[brunette15]

I am attempting to find the determinant using gaussian elimination for the following matrix [4 3 2; 1 7 8; 3 9 3].
I have begun by attempting to form zeros below the diagonal. The answer should be -165, however i keep getting values up to -665. I have tried a variety of times and keep getting really big numbers :/

 

[chisigma]

I am attempting to find the determinant using gaussian elimination for the following matrix [4 3 2; 1 7 8; 3 9 3].
I have begun by attempting to form zeros below the diagonal. The answer should be -165, however i keep getting values up to -665. I have tried a variety of times and keep getting really big numbers :/

Your matrix is [4 3 2; 1 7 8; 3 9 3]...

a) divide the first row by 4 and subtract it fron the second row obtaining [4 3 2; 0 25/4 15/2; 3 9 3]...

b) multiply the first row by 3/4 and subtract it from the third row obtaining [4 3 2; 0 25/4 15/2; 0 27/4 3/2]...

c) multiply the second row by 27/4 and subtract it from the third row obtaining [4 3 2; 0 25/4 15/2; 0 0 -33/5]...

d) the determinant is d= 4 25/4 (- 33/5) = - 165...

kind regards

$\chi$ $\sigma$

 

[soroban]

Hello, brunette15!

Find the determinant using Gaussian elimination: .$$\begin{vmatrix} 4&3&2 \\ 1&7&8 \\ 3&9&3 \end{vmatrix}$$

I have begun by attempting to form zeros below the diagonal.
The answer should be -165; however, i keep getting values up to -665.
I have tried a variety of times and keep getting really big numbers.

If you show us your attempts, we can point out your errors.

$$\;\;\begin{array}{c}\text{Given:}\end{array} \;\begin{vmatrix} 4&3&2 \\ 1&7&8 \\ 3&9&3 \end{vmatrix}$$

$$\begin{array}{c}R_1-R_3 \\ \\ \\ \end{array}\;\begin{vmatrix}1&\text{-}6&\text{-}1 \\ 1&7&8 \\ 3&9&3 \end{vmatrix}$$

$$\;\;\;\;\;\begin{array}{c}\\ \\ \frac{1}{3}R_3 \end{array} \; \begin{vmatrix} 1&\text{-}6&\text{-}1 \\ 1&7&8 \\ 1&3&1 \end{vmatrix}\;\cdot\;(3)$$

$$\begin{array}{c}\\ R_2-R_1 \\ R_3-R_1 \end{array}\;\begin{vmatrix}1&\text{-}6&\text{-}1 \\ 0&13&9 \\ 0&9&2\end{vmatrix}\;\cdot\;(3)$$

$$\;\;\;\;\begin{array}{c}\\ \frac{1}{13}R_2 \\ \\ \end{array} \;\begin{vmatrix} 1&\text{-}6&\text{-}1 \\ 0&1&\frac{9}{13}\\0&9&2 \end{vmatrix}\;\cdot(3)\cdot(13)$$

$$\begin{array}{c}\\ \\ R_3-9R_2\end{array} \; \begin{vmatrix} 1&\text{-}6&\text{-}1 \\ 0&1&\frac{9}{13} \\ 0&0&\text{-}\frac{55}{13}\end{vmatrix}\;\cdot (3)\cdot(13)$$$$\;\;(1)(1)(\text{-}\tfrac{55}{13})\cdot (3)(13) \;=\; -165$$