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SupaNerd
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Hey thanks again, figured these questions out!
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SupaNerd said:1) Find a basis of R^4 that contains the vectors [ 1 2 3 4 ] and [ 0 1 0 1].
Note, they are both column vectors but I do not know how to orient them on this site.
2) Find a non linear function f : R^2 ---- > R^2
that still satisfies,
f(rv) = rf(v) for all r and all v.
A permutation matrix is a square matrix that represents a permutation of a set of numbers. It is used in linear algebra to perform row and column operations on matrices, which can be useful in solving systems of linear equations and finding inverse matrices.
A basis is a set of linearly independent vectors that can be used to represent and span a vector space. It is important in linear algebra because it allows us to represent and manipulate vectors and matrices in a more efficient and concise way, and it also helps us understand the structure of vector spaces.
Permutation matrices are not directly related to non-linear functions. However, they can be used in conjunction with other matrices to perform operations on non-linear functions, such as transforming them into linear functions for easier analysis.
No, permutation matrices are generally used for linear operations and are not suitable for solving non-linear equations. Other techniques, such as substitution or iteration methods, are typically used for solving non-linear equations.
One limitation of permutation matrices is that they can only be used for square matrices, meaning that the number of rows and columns must be equal. Additionally, they can only be used for operations that preserve the number of rows and columns, such as row and column swaps, and cannot be used for operations like scalar multiplication or addition.