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kayvan momeni
Nikc M
November 16, 2017
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
[…]
November 16, 2017
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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November 12, 2017
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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November 2, 2017
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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October 9, 2017
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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October 3, 2017
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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September 28, 2017
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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September 21, 2017
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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September 6, 2017
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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August 21, 2017
Matrix Inverse
Example 1. We want to find inverse of the matrix (1) This means we want to find a matrix such that (2) We start
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August 18, 2017
Matrix & Basic Operations
Suppose (1) and we would like to compute when possible. Let’s begin with the first one (2) Next, we know multiplying two
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August 12, 2017
Linear System and Matrix
Example 1. We are given the system (1) The matrix associated to this system is (2) We want to find the solution set of
[…]
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