Linear Algebra Midterm 2 Review

Get ready for your Linear Algebra Midterm 2 with this in-depth review session! We cover a wide range of crucial topics, including:

Solution sets of linear systems (homogeneous and nonhomogeneous)
Balancing chemical equations using linear algebra
Introduction to linear transformations and standard matrices
Matrix operations and properties of matrix multiplication
Inverse of a matrix and the Invertible Matrix Theorem
Determinants of 2x2, 3x3 matrices, and beyond, including properties and cofactor expansion
Properties of determinants, including row reduction to echelon form
Vector spaces, subspaces, and how to determine if a set of vectors is a basis
Geometric linear transformations such as reflections, projections, and rotations
Matrix equations and solving for unknowns

We’ll break down complex problems into manageable steps. Whether it's matrix inverses, transformations, or determining if a set of vectors forms a basis, this video will guide you through everything you need to succeed on your midterm.

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*Timestamps*
00:00 Introduction
00:40 Section 1.5 - Solution Sets of Linear Systems
04:27 Section 1.6 - Balancing Chemical Equations
05:50 Section 1.8 - Introduction to Linear Transformations
09:44 Section 1.9 - Standard Matrix of a Linear Transformation
13:13 Section 2.1 - Matrix Operations
16:25 Section 2.2 - Inverse of a Matrix
20:55 Section 2.3 - Invertible Matrix Theorem
24:07 Section 3.1 - Calculating Determinants
27:57 Section 3.2 - Properties of Determinants
29:00 Section 4.1 - Vector Spaces and Subspaces
31:28 Section 4.3 - Basis of a Vector Space

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Understand The Math provides students and lifelong learners with access to free, straightforward, and engaging mathematics instruction. I’m Cheryl Hile, the founder of Understand The Math, and I’m passionate about ensuring that accurate and engaging mathematics instruction is available to everyone! I have a Ph.D. in Engineering Science and Applied Mathematics and have over 25 years of teaching experience at the university level. This channel provides videos that contain clear explanations, step-by-step problem solving strategies, and carefully worked out example problems. In the video descriptions, you'll find a link to free guided notes. Students can use these notes to highlight concepts and fill in answers to example problems while watching the videos, and later, they can review what they've learned.

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