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What does the discriminant tell you when solving quadratic equations for the roots?
Whether the equation has 2 distinct roots, repeated roots, or complex roots. If the determinant is smaller than 0 then it has complex roots. If the determinant is 0 then it has repeated roots. If the determinant is greater than 0 then it has two distinct roots.
A rectangular arrangement of numbers in rows and columns?
It is a matrix or a determinant.
What is the maximum determinant in an 8 by 8 matrix of zeros and ones?
56
What is jacobian ratio?
Jacobian Ratio The Jacobian calculation is done at the integration points of elements commonly known as Gauss Point. At each intergration point, Jacobian Determinant is calculated, and the Jacobian ratio is found by the ratio of the maximum and minimum determinant value. The Jacobian Determinant of 2D elements is calculated after it has been projected on to a plane, and the determinant of 3D elements is found by direct calculation. If the quadrilateral element is not convex, the negative Jacobian ratio will be obtained, and elements with the negative Jacobian Ratio can not be solved with correct result.
How do you show a matrix is invertible?
For small matrices the simplest way is to show that its determinant is not zero.
