THIS LECTURE WE HAVE MADE TO QUALIFY GATE EXAM,
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At first the mathematician made the linear equations when we had more than one equations and unknown then we used the matrix technology to find weather such linear equations has solutions exist or not?
A System of linear equations can be represented in matrix form using a coefficient matrix, a variable matrix, and a constant matrix.
Consider the system,
2x+3y=8
5x−1y=−2
The coefficient matrix can be formed by aligning the coefficients of the variables of each equation in a row. Make sure that each equation is written in standard form with the constant term on right.
Then, the coefficient matrix for the above system is
2 5
3 -1
The variables we have are x and y . So we can write the variable matrix as
[x y] .
On the right side of the equality we have the constant terms of the equations,
8 and −2 . The two numbers in that order correspond to the first and second equations, and therefore take the places at the first and the second rows in the constant matrix. So, the matrix becomes
[ 8
−2 ].
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