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kayvan momeni
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Power Series
Example 1. We want to find all numbers for which the power series (1) converges. Define for every and use Ratio test to write
[…]
Eigenvalues and Eigenvectors
Example 1. Suppose we are given the map defined by . We would like to check if is linear. Take two vectors and and write
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Gram-Schmidt Process
Gram-Schmidt Process, Orthonormal Basis Example 1. We are given the set . First we notice that (1) and therefore the two vectors in this
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Rank and Nullity
Rank and Nullity Example 1. We want to find a basis for the row space of (1) We know the row space of is
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Linearly Independent Sets and Basis
Linearly Independent Sets and Basis Example 1. Suppose we are given the set . We would like to determine if this set is linearly independent.
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Vector Space
Vector Space Example 1. We are given a vector where and are real numbers. We would like to write as a linear combination of vectors and
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More on Determinants
More on Determinants Observation 1. We are given two matrices and . Assume that matrix is elementary. Case 1. is obtained from by interchanging
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Determinants
Example 1. We would like to find the determinant of (1) We write (2) Example 2. We would like to find the determinant
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Elementary Matrices
Example 1. Suppose we want to find a sequence of elementary matrices that can be used to write (1) in row-echelon form. We know an
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