Using elimination method is not giving the expected results

Hello everyone.

I was watching the the “Matrix Inverse” video and I do not understand how the equations (shown in screenshot) are being solved. I tried elimination method but my results are different from the ones in the video.

Kindly someone explain what am I doing wrong.

Thank You

Screenshot:

Hello @annoyingCode I assume you’re asking how to find the values of the constants a,b,c,d?
I haven’t checked the video on the methods that was used but here is a basic one:

  1. Let take 2 equations with common constants.
  • 3a + 1c = 1

  • 1a + 2c = 0

  1. Firstly, multiply both the given equations by some suitable non-zero constants to make the coefficients of any one of the variables (either a or c) numerically equal.
  • (3a + 1c = 1)2 ===> 6a + 2c = 2

  • (1a + 2c = 0)1 ===> 1a + 2c = 0

  1. After that, add or subtract one equation from the other in such a way that one variable gets eliminated.
  • 6a + 2c = 2

  • 1a + 2c = 0

(6a - 1a = 5a), (2c - 2c = 0), = (2 - 0 = 2) Hence

  • 5a = 2

  • a = 2/5

  1. Substitute this value in any of the given equations to get the value of another variable
  • 1(2/5) + 2c = 0

  • 2c = -(2/5)

  • c = -(1/5)

Repeat the same process to find b and d

Let me know if this is what you were asking?

1 Like

Thank You so much for the reply.

Yes, I am asking the exact thing that you mentioned. Turns out, I was also doing the same except that I was taking the LCM wrong (a subtle mistake) but I am glad that I was able to find the error.

Thank You for the help. I really appreciate it.

Welcome @annoyingCode . Happy to hear you have figured it out

Happy learning
Isaak Kamau