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How To - Determinants of Matrices

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The determinant of a matrix is very useful and commonly asked for in exams. With it, you can determine if a matrix is invertible (thus find the inverse for sure, without wasting tons of precious time in an exam) and it's a sure way to get points even if you are pretty hopeless and just want to pass There are three basic cases for matrices, dimensions 2x2 , 3x3 and dimensions 3< . Results for the three exercises will be posted at the end. Tipp : a matrix can only be inverted if the determinant does not equal 0 ! In the case of matrix A (2x2) the main- minus minor-diagonal formula applies; with upper left times lower right, minus upper right times lower left. For example B (3x3) it becomes more complicated. We can apply the rule of Sarrus ( Wikipedia ). For that, we replicate the first two columns to the right side. Now we create the main and minor diagonals, as seen in the picture below: After this, we subtract the sum of the minors from the sum of the

How To - Citric Acid Cycle

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The citric acid cycle is one of the central logistical hub in our metabolism. It provides oxidative breakdown for organic substances, energy by releasing CO2 and H2O from Acetyl-CoA and so on. There are 10 basic steps to the cycle and its goal is to catalyze the condensation of Oxalacetate to Citrate. I will list the  intermediates of this reaction and their respective enzymes , as well as their components : Citrate  + Aconitase -> cis-Aconitate   ( H20) cis-Aconitate + Aconitase ->  Isocitrate    ( H20) Isocitrate  + Isocitrate-dehydrogenase -> Oxalsuccinate    (NAD+, NADH) Oxalsuccinate  + Isocitrate-dehydrogenase -> Alpha-ketoglutaric-acid   (CO2) Alph a-ketoglutaric-acid  + alpha-ketoglutarate-dehydrogenase-complex -> Succinyl-CoA   (CoA, NAD+, CO2, NADH/H+) Succinyl-CoA  + Succinyl-CoA-Synthase -> Succinate  (GDP, ADP, GTP, ATP) Succinate  + Succinate-dehydrogenase -> Fumarate   (FAD, FADH2) Fumarate  + Fumaras