invertible definition

The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B =..

The adjoint of a square matrix [aij] is defined as the transpose of the matrix [Aij] where Aij are the cofactors of the elements aij. Adjoint of A is denoted by adj A. Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, where I is..

Question: Define magnification. Answer: The ratio of the height of the image to the height of the object is called the linear magnification. For a real image u and v are negative and the magnification is negative. Negative magnification means the image is inverted. ..

Ecological Pyramids - Ecological pyramids are also called 'Eltonian pyramids' after C. Elton. Charles Elton (1927) developed the concept of ecological pyramids who noted that "the animals at the base of a food chain are relatively abundant while those at the end are relatively few in number" Ecolog..

The light coming from an object enters the eye through cornea and pupil. The eye lens converges these light rays to form a real, inverted and diminished image on the retin..

The image is - formed at 2F 2 real inverted same size as the objec..

"Pyramid of biomass is the graphic representation of biomass present per unit area of different trophic levels, with producers at the base and top carnivores at the tip". The total amount of living or organic matter in an ecosystem at any time is called 'Biomass'. In a terrestrial ecosystem, the ma..

If A and B are two invertible matrices of the same order, then (AB) - 1 = B - 1 A - 1..

If A and B are two invertible matrices of the same order, then (AB) - 1 = B - 1 A - 1..

Pyramid of Biomass - "Pyramid of biomass is the graphic representation of biomass present per unit area of different trophic levels, with producers at the base and top carnivores at the tip". The total amount of living or organic matter in an ecosystem at any time is called 'Biomass'. In a terrestr..