About This Chapter
How it works:
- Identify which concepts are covered on your vectors, matrices and determinants homework.
- Find videos on those topics within this chapter.
- Watch fun videos, pausing and reviewing as needed.
- Complete sample problems and get instant feedback.
- Finish your vectors, matrices and determinants homework with ease!
Topics from your homework you'll be able to complete:
- Operations on vectors in the plane
- The dot product of vectors
- Augmented matrices
- Matrix row operations
- Inverse matrices
- Gaussian elimination
- Gauss-Jordan elimination
- Inconsistent and dependent systems
- Multiplicative inverses of matrices
- The determinant of a matrix
- Higher-order determinants
- Cramer's rule
1. Performing Operations on Vectors in the Plane
After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.
2. The Dot Product of Vectors: Definition & Application
After watching this video lesson, you will be able to find the dot product of vectors both algebraically and geometrically. Learn the difference between the two and what you need in order to calculate them.
3. What is a Matrix?
As math gets more and more complicated and there become more and more numbers flying around, it becomes really handy to put all these numbers in a nice organized grid... hello matrices! Learn about what they are and why there are used.
4. How to Write an Augmented Matrix for a Linear System
Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.
5. How to Perform Matrix Row Operations
Watch this video lesson to learn how easy it is to perform row operations on a matrix. Learn how to perform the three basic operations easily and quickly.
6. Matrix Notation, Equal Matrices & Math Operations with Matrices
Watch this video lesson to learn about the basics of matrices and what kinds of math operations you can do with them. Also learn how to determine whether two matrices are the same or not.
7. How to Solve Inverse Matrices
Watch this video lesson to learn what kinds of matrix operations you can take to find the inverse of a matrix. Also learn why matrix inverses are useful.
8. How to Solve Linear Systems Using Gaussian Elimination
Watch this video lesson to learn an easy way to solve a system of equations that involves manipulating a matrix. Learn the kinds of easy matrix manipulations that are needed to solve any system of equations.
9. How to Solve Linear Systems Using Gauss-Jordan Elimination
You will come across simple linear systems and more complex ones as you progress in math. Watch this video lesson to learn how you can use Gauss-Jordan elimination to help you solve these linear systems.
10. Inconsistent and Dependent Systems: Using Gaussian Elimination
Watch this video lesson to learn whether or not you can use Gaussian elimination to solve inconsistent and dependent systems. Also, learn whether there is another way to find solutions of these systems.
11. Multiplicative Inverses of Matrices and Matrix Equations
Watch this video lesson to learn about another method you can use to solve a matrix problem if you are given the inverse of the matrix. You will also learn the identifying mark of the multiplicative inverse of a matrix.
12. How to Take a Determinant of a Matrix
Matrices are incredibly powerful and can help you do all sorts of things, but one of the most basic (and surprisingly helpful) operations you can perform on one is to take its determinant. Learn how to do that here!
13. Solving Systems of Linear Equations in Two Variables Using Determinants
Watch this video lesson to learn how you can easily find the solution of a linear system in two variables by just using determinants. All you need to find the complete solution is to find three determinants.
14. Solving Systems of Linear Equations in Three Variables Using Determinants
Watch this video lesson to learn how to use Cramer's rule to help you find your solutions by finding just four determinants. Learn the numbers to use for your determinants.
15. Using Cramer's Rule with Inconsistent and Dependent Systems
Watch this video lesson, and you will see what happens when we use Cramer's Rule with inconsistent and dependent systems. You will see what kind of result you will always get when you try to use Cramer's Rule.
16. How to Evaluate Higher-Order Determinants in Algebra
Watch this video lesson to learn the rules for taking the determinant of any size matrix. Learn the kind of matrix that you need before you can take the determinant. Watch as the pattern of the determinant takes shape.
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Other chapters within the High School Precalculus: Homework Help Resource course
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