Rank of a matrix is used to find consistency of linear system of equations.As we know most of the engineering problems land up with the problem of finding solution of a linear system of equations ,at that point rank of matrix is useful.
Cramer's Rule is a method for using Matrix manipulation to find solutions to sets of Linear equations.
The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.
Larry Freeman has a very nice proof ( one you can find in most linear algebra texts) on his blogspot.I encourage you to look at it and go over it line by line.http://mathrefresher.blogspot.com/2007/06/column-space.html
Write an algorithm to find the root of quadratic equation
Find directed graph that has the adjacency matrix Find directed graph that has the adjacency matrix
To find the roots (solutions) of a quadratic equation.
To find the original matrix of an inverted matrix, simply invert it again. Consider A^-1^-1 = A^1 = A
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
I suggest you use the quadratic formula.
When an equation cannot be solved for "x" to find the zeroes, the quadratic formula can be used instead for the same purpose.
For any quadratic ax2 + bx + c = 0 we can find x by using the quadratic formulae: the quadratic formula is... [-b +- sqrt(b2 - 4(a)(c)) ] / 2a