Second Midterm, Copy 1

Elementary Calculus Second Midterm, Copy 1 1. Differentiate (1)   Solution: We know (2)   We can use product rule to write (3)     We […]

Elementary Calculus, First Midterm, Copy 2

Elementary Calculus, First Midterm, Copy 2 1. Suppose is a given function and and are real numbers. State what we mean by (1)     Solution: […]

Elementary Calculus, First Midterm, Copy 1

Elementary Calculus, First Midterm, Copy 1 1. Suppose is a given function and is a real number. State what we mean by (1)     Solution: […]

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 […]

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 […]

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 […]

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. […]

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 […]