determinant area 16 videos

Area With Determinants
Precalculus Systems of Linear Equations and Matrices
How to compute the area of a parallelogram using a determinant.
parallelogram vectors determinant area 
2x2 Determinants
Precalculus Systems of Linear Equations and Matrices
How to compute the determinant of a 2x2 square matrix.
square matrices determinant 2x2 determinant 
3x3 Determinants
Precalculus Systems of Linear Equations and Matrices
How to compute the determinant of a 3x3 square matrix using minors by expanding along the top row.
square matrices determinant 3x3 determinant minor of an element 
Invertible Square Matrices and Determinants
Precalculus Systems of Linear Equations and Matrices
How to determine whether a square matrix is invertible using its determinant.
square matrices invertible determinant zero determinant inverse of a 2x2 matrix 
Simplifying Determinants
Precalculus Systems of Linear Equations and Matrices
How to simplify determinants using three row (or column) operations.
determinant row operations column operations interchanging rows common factors adding a multiple of one row to another 
Using Sine to Calculate the Area of a Triangle
Precalculus Basic Trigonometry
How to calculate the area of any triangle using two sides and an included angle.
area of a triangle sine 
Area With the Cross Product
Precalculus Systems of Linear Equations and Matrices
How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.
cross product magnitude of vectors dot product angle between vectors area parallelogram 
The Cross Product of Vectors
Precalculus Systems of Linear Equations and Matrices
How to compute the cross product of two 3D vectors.
unit vectors components cross product determinant 
Cramer's Rule
Precalculus Systems of Linear Equations and Matrices
How to solve a system of two linear equations with two unknowns using Cramer's rule.
systems of linear equations Cramer's rule determinant coefficient matrix 
The Identity Matrix
Precalculus Systems of Linear Equations and Matrices
How to determine the identity matrix of order n.
matrices square matrices the identity matrix matrix multiplication 
The Inverse of a Square Matrix
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices are inverses.
matrices square matrices the identity matrix matrix multiplication invertible inverse matrix 
Perpendicular, Parallel and Skew Lines in Space
Precalculus Vectors and Parametric Equations
How to determine whether two lines in space are parallel or perpendicular.
perpendicular lines dot product direction vectors parallel lines scalar multiple skew lines 
Symmetry of Polar Graphs
Precalculus Polar Coordinates and Complex Numbers
How to determine if the graph of a polar equation is symmetric about the xaxis.
polar graph polar equation symmetry reflection x axis symmetric about the x axis 
The Angle Between Planes
Precalculus Vectors and Parametric Equations
How to find the angle between planes, and how to determine if two planes are parallel or perpendicular.
normal vector the angle between planes perpendicular planes dot product scalar multiple parallel planes 
Square Matrices
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices can be multiplied, and if so, what the dimensions of the product will be.
matrices rows columns dimension matrix multiplication 
The Transformation y = f(bx)
Precalculus Introduction to Functions
How determine what transformation the graph y = f(bx) represents when b > 1.
the square root function horizontal shift horizontal compression compression factor endpoint