$$A=\begin{pmatrix}4x+24 & x-12 & x-12 & x-12 & x-12\\x-12 & 4x+24 & x-12 & x-12 & x-12\\x-12 &x-12 &4x+24 & x-12 & x-12\\x-12 & x-12 & x-12 & 4x+24 & x-12\\ x-12 & x-12 & x-12 & x-12 & 4x+24\end{pmatrix}$$ Given the matrix above, what is the easiet way to calculate its determinant? I've tried getting as many zeroes on the first column for example, but I still end up with 2 non-zero elements. And it repeats for every minor, and becomes very tedious. Any help would be appreciated.
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Please don't use pictures of text or formulas. See here, why. Use MathJax. Here is a tutorial. For such matrices there is a general formula for its determinant - search it! – Dietrich Burde Mar 29 '24 at 15:17
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I would start by subtracting the first column from all the others. – Ethan Bolker Mar 29 '24 at 15:18