3 x 3 determinant  Matrix transformations  Linear Algebra  Khan Academy  Summary and Q&A
TL;DR
Determinants are used to determine if a matrix has an inverse and can be computed using specific formulas.
Key Insights
 โ The determinant of a matrix is used to determine if the matrix has an inverse.
 ๐ซ The formula for the determinant of a 2x2 matrix is ad  bc.
 ๐ป The determinant of a 2x2 matrix is computed using specific entry combinations.
 ๐คจ The determinant of a 3x3 matrix is computed by expanding along the first row and recursively finding the determinant of submatrices.
 โ The determinant of a 3x3 matrix determines if the matrix is invertible.
 ๐ป The determinant of a 3x3 matrix can be computed using specific entry combinations.
 โ The determinant of a matrix is an important concept in linear algebra.
Transcript
In the last video we defined the notion of a determinant of a 2 by 2 matrix. So if I have some matrix let's just call it B if my matrix B looks like this, if its entries are a, b, c, d, we've defined to determinant of B. Which could also be written as B with these lines around it, which could also be written as the entries of the matrix with th... Read More
Questions & Answers
Q: What is the determinant of a 2x2 matrix?
The determinant of a 2x2 matrix is computed using the formula ad  bc.
Q: How is the determinant related to finding the inverse of a matrix?
The determinant of a matrix is used to determine if the matrix has an inverse. If the determinant is not zero, the matrix is invertible.
Q: How is the determinant of a 3x3 matrix computed?
The determinant of a 3x3 matrix is computed by expanding along the first row and recursively finding the determinant of the resulting 2x2 submatrices.
Q: What does the determinant of a 3x3 matrix indicate?
The determinant of a 3x3 matrix determines if the matrix is invertible. If the determinant is not zero, the matrix is invertible.
Summary & Key Takeaways

An explanation of the determinant of a 2x2 matrix and its formula: ad  bc.

The determinant of a 2x2 matrix determines if the matrix is invertible.

Introduction to the determinant of a 3x3 matrix and its computation.