# Thread:

1. ## [SOLVED] Determinant of a 3x3 matrix

I've done the problem but I just want to know if I'm on the right track because I've solved many others this way. In other words, is my answer correct?
Determine for which values of $c$ the following matrix is invertible :
$\left[ \begin{array}{ccc} 1 & c & -1 \\ c & 1 & 1 \\ 0 & 1 & c\end{array} \right]$.
From my memory I think that this holds : A matrix $A$ is invertible if and only if its determinant is different from $0$. So I calculated the determinant of the matrix above to be $-1-c^3$, from which I concluded that the matrix is invertible $\forall c \in \mathbb{C}$ such that $c\neq -1$.

2. You correctly calculated the determinant and your statement about the matrix's invertibility is true.

3. Originally Posted by icemanfan
You correctly calculated the determinant and your statement about the matrix's invertibility is true.
Youpi!!!
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9456110596656799, "perplexity_flag": "head"}