How to determine if a matrix is linearly independent? How can you determine if a matrix is linearly independent? How to determine if matrices are linearly independent? How to determine if a set is linearly inde
First we need to understand the determinant of a matrix to understand the singular or aij denotes the element of ith row and jth column Sign system for expansion of determinant: If i + j is even then sign will be positive. if i + j is odd then sign will be negative. like as, ...
Find the determinant of the matrix. If and only if the matrix has a determinant of zero, the matrix is singular. Non-singular matrices have non-zero determinants. Step 2 Find the inverse for the matrix. If the matrix has an inverse, then the matrix multiplied by its inverse will give yo...
How to tell if a set is transitive? Explain what is an equal and unequal set. Give relevant example along with. Define f(x) = e^(-1/x^2), x is not equal to 0, 0, x = 0. Show that f prime(0) exists. Determine whether the set S=\left \{ \begin{bmatrix} 1\\ 0...
In some naturally fractured reservoirs, if the micro fractures or secondary fractures are well-connected, then the effective formation permeability is controlled by both the stimulated natural fractures and rock matrix. Significant progress has been made on the mechanism of hydraulic fracture propagation ...
where ω is the frequency, kB is the Boltzmann constant, t is the correlation time, and Tr is the trace matrix operator, \(\bar{\alpha }\) and β are the isotropic and anisotropic components of the polarizability tensor α: \(\bar{\alpha }=\frac{1}{3}{\rm{Tr}}\alpha\) and \...
The matrix .J is operator valued and depends on the state. .J can be explicitly derived using reduction theorems, following Marsden and Weinstein [1974], Holm et al. [1998]. We speak of Hamiltonian dynamics if the evolution of a functional F is expressed by d . F = −{F, H }, ...
less than 1. Due to the constraints of only interacting with neighbours,\(p_{ij} > 0\)if\((v_i,v_j) \in E\). Each interaction is characterised by the\(n \times n\)matrix of the averaging weights\({\textbf {W}} = [w_{ij}]\), so that the vector of values is updated ...
Cell spreading, the process through which newly attached cells encounter and engage theextracellular matrix(ECM), is a crucial prerequisite for cell migration and requires the coordination of the same subcellular processes. Investigation of the initiation and control of spreading has therefore yielded val...
Determine whether the statement, if AB is invertible, A and B are invertible matrices, is true or false. Invertible Matrix: An invertible matrix is one that has a pair of matrices called the inverse matrix, such that when multiplied in any order, either...