What Can Determinants Do? | Cramer’s Rule, Geometry & More

In this Linear Algebra lesson, we move beyond calculating determinants and explore several important applications of determinants. We use determinants to find matrix inverses, solve systems of linear equations, and solve geometric problems involving areas, volumes, lines, and planes. Topics covered: Finding the adjoint (adjugate) of a matrix Using the adjoint to find a matrix inverse Cramer’s Rule for solving systems of linear equations Finding the area of a triangle using determinants Finding the volume of a tetrahedron Finding equations of lines using determinants Finding equations of planes using determinants Worked examples This lesson brings together many of the determinant concepts from the previous videos and shows how they can be used to solve problems throughout Linear Algebra and geometry. Playlist: https://bit.ly/4qtJZ6r #linearalgebra #determinants #cramersrule #adjoint #Adjugate #matrices #geometry #matrixinverse #collegemath #mathtutorial