MATH MAANIAC

Let's start with a question, "Can I be in a different position at the same time ?" Obviously - No. Ok, let's ask the question more specifically, "Can I be in a mood of happy and sad at the same time ?"  🤔🤔🤔 Well, we can say many times in life we are not actually happy or sad, if we try to measure on a scale starting 1 with sadness and 10 with happiness, we may be in between 1 and 10. Let at 1 sad,  2 - 4 is more likely sad, 5,6 neither happy nor sad,  7 - 9  is more likely happy and at 10 is happy. Have a look at the following table and graph - (Scores actually represent inner psychological feelings) So for the whole day, since the average of all scores is 7, we can say more likely happy is the experimented mood, but if we see the data locally it does not say so, it can say we are in some ups and down combination of happy and sad (like a wave spread in a whole day). Two clever observations I would like to mention here, 1. As I mentioned earlier, although

                   Linear Algebra is the most useful and powerful tool in Mathematics. In the last blog " Linear Algebra - Purpose to Application " we saw how a higher-order system of linear equations has been solved by transforming the equation into the matrix.                  Although it's good to mention that it only works if in the AX=B [A is m*n, X is n*1, B is m*1, so it has m equations and n unknowns ]  our A matrix is invertible, if it is not invertible i.e, in the sense of matrix it is rank of A is less than n and rank of (A;B) = rank of A < n, so the system of linear equation AX=B has infinitely many solutions, we can find the solution by converting the A matrix into row-echelon form, simply you will get the solution from bottom.         Note:-  1. The rank of a matrix - It is defined as the largest order square matrix whose determinant is non-zero.                   2. Row-echelon form - We said a matrix is in a row echelon form if in the matrix fo