Blog 9
Midterm II Preparation Materials
Midterm 2 : Overview
Topics: Beginning up to Midterm 2
1) System of Equations
2) Gaussian Elimination
3) Rank of a Matrix
4) Linear Combinations
5) Spans
6) Vector & Linear Independence
7) Basis & Dimensions
8) Subspaces
9) Matrix Algebra
10) Linear Transformations
11) Image
12) Kernel
13) Compositions
14) Rank-Nullity Theorem
15) Inverses
16) Coordinates
17) Coordinates for transformations
Extra Practice:
System of Equations
Exercise: https://www.math-exercises.com/matrices/system-of-equations-solved-by-matrices
Gaussian Elimination
Exercise:
(1) https://courses.lumenlearning.com/sanjacinto-finitemath1/chapter/2-5-exercisesaugmented-matrices/
(2) https://home.cc.umanitoba.ca/~thomas/Courses/RREF_Practice.pdf
Rank of a Matrix
https://www.math-exercises.com/matrices/rank-of-a-matrix
Solutions: Unique, Consistency, Inconsistency
Vector Addition
Linear Combinations
(1) https://onlinemschool.com/math/library/vector/linear-independence/
(2) https://www.math.colostate.edu/~aristoff//369_HW15.pdf
Vector & Linear Independence
https://onlinemschool.com/math/practice/vector2/multiply/
https://onlinemschool.com/math/practice/vector3/multiply1/
Matrix Algebra
(1) https://www.shmoop.com/matrices/adding-subtracting-exercises.html
(2) https://www.shmoop.com/matrices/multiplying-matrix-exercises.html
Linear Transformations
https://yutsumura.com/tag/linear-transformation/