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Could someone tell me what I'm doing wrong? I'm learning cramer's rule and I'm trying to find X1. I understand how they found the determinant of the first matrices. When finding the determinant of the matrice for X1 my process is different. I did row operation to simplify calculations first, then found determinant as -1, but the correct answer is 1. My steps are given in the lined piece of paper. What's wrong?

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Compsci
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2 Answers2

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Your mistake is the first step as you multiply $-3$ to the first row and add it to the second row.

The $(2,2)$-entry should be negative, $-7$ rather than $7$.

Siong Thye Goh
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  • I did 3r1 -r2 , isn't that allowed? – Compsci Jul 11 '17 at 01:10
  • That would be equivalent to first multiply the second row by $-1$. (hence the extra negative sign). Then perform $r_2+3r_1$. – Siong Thye Goh Jul 11 '17 at 01:11
  • Ah I see, so I cannot multiply second row with a constant if I'm modifying it. Got it, I made the same mistake yesterday. Thanks a lot. – Compsci Jul 11 '17 at 01:12
  • yup, sticking to the convention of $R_i \leftarrow R_i + c R_j$, avoiding any other coefficient besides $1$ for $R_i$ might reduce some computational mistakes. – Siong Thye Goh Jul 11 '17 at 01:15
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I assume you simplified using in the following manner: $$ R_2 \Rightarrow R_2 -3R_1 $$

If so, consider that cell $ (2,2) $ should be equal to $ -3a_{1,2} + a_{2,2} = -3*2-1 = -7 $ whereas in your notebook you mistakenly wrote $ +7 $

I suppose this accounts for the wrong sign :P

Pit Omer
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