- #1
Ted123
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Homework Statement
[PLAIN]http://img697.imageshack.us/img697/9307/linvd.jpg
The Attempt at a Solution
Last condition = 1) ?
How about the others?
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lanedance said:so how about starting by finding the eigenvalues?
lanedance said:ok, so you have the general formula, but finding the eigenvalues for each case, should give you good hint...
if you're not sure why try reading
http://en.wikipedia.org/wiki/Diagonalizable_matrix
lanedance said:for the last one, a^2 - 4b < 0 is a subset, but more importantly consider when a^2 - 4b = 0
Linear algebra is a branch of mathematics that deals with the study of linear equations and their relationships through the use of matrices and vectors.
Linear algebra has many applications in various fields including engineering, physics, computer graphics, economics, and data analysis. Some examples include image and signal processing, optimization problems, and machine learning algorithms.
The basic operations in linear algebra include addition and subtraction of matrices, multiplication of a matrix by a scalar, and matrix multiplication. These operations are used to solve systems of linear equations and manipulate data in various applications.
A vector is a one-dimensional array of numbers, while a matrix is a two-dimensional array of numbers. Vectors can be thought of as a special case of matrices, where one dimension is equal to 1.
Linear algebra plays a crucial role in machine learning algorithms such as linear regression, support vector machines, and artificial neural networks. It is used to represent and manipulate data, as well as to optimize parameters in these algorithms.