Does every matrix have a reduced row echelon form? Reduce the matrix to reduced row echelon form. A = 4 -1 16 1 3 4 Does row reduction change eigenvalues? Compute the row reduced echelon form of the matrix. A=\begin{bmatrix} 2 & -1 & -1 & 3 & 0 & 1\0 & 2 & 2 & 2 &...
How many Eigenvectors does a matrix have?Eigenvectors:In 3D space matrices represent a way to stretch, shear or squish, rotate that space, by multiplying every vector in that space. But, at the same time it would be useful to find out such vectors in that space which do not change ...
used to define a vector space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector. ... Thus, for example, the product of a 1 × n matrix and an n × 1 matrix, which is formally a 1 × 1 matrix, is often said to be a ...
When multiple traits are selected, the mean changes in proportion to the additive genetic covariance matrix (termed the ‘G matrix’) that in turn is proportional to the mutational covariance in the infinitesimal limit. The G matrix has received much attention on the grounds that it constrains ad...
Why do symmetric matrices have orthogonal eigenvectors? Given matrix A , explain when this matrix can be diagonalized. If A is a 6x5 matrix with a pivot in every column, is A invertible? why or why not? The given matrices are A = (2, - 5; - 1, 3), B = (1, - 1, 3; 2,...
Math Algebra Eigenvalues and eigenvectors For what value of k does the matrix A = [1, k; 1, -7] have one real eigenvalue of multiplicity 2?...Question:For what value of k does the matrix A = [1, k; 1, -7] have one real eigenvalue of mul...
The vector or the matrix can be linearly dependent or can be linearly independent. So we can have the column or row dependent or independent. There can be a diagonal matrix and the orthogonal matrix too.Answer and Explanation: Become a member and unlock all Study Answers Start today. Try ...
Does a matrix and its transpose have the same eigenvectors? How do you find the elementary matrix for a non-square matrix? Can a matrix squared make the identity matrix? Orthogonally diagonalize the matrix A = (6 2 2 6). That is, find an orthogonal matrix P such that P^TAP is a dia...
Given a matrix: a= \begin{pmatrix} 1& \alpha &0\\beta &1&0\0&0&1 \end {pmatrix} where \alpha and \beta are non-zero complex numbers, find its eigenvalues and eigenvectors. Find the respective conditions for: a) the eigenvalues to be real and b) t...
It can be seen that the orthogonal matrix that transforms 𝑦𝑖yi into 𝑧𝑖zi is none other than the transpose of the matrix whose columns are the normalized eigenvectors of the variance–covariance matrix of the original dataset. When the variables present significantly different variances, ...