# 19. Determinant Formulas and Cofactors | Summary and Q&A

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May 7, 2009
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MIT OpenCourseWare
19. Determinant Formulas and Cofactors

## TL;DR

Linear algebra's determinants are a small but fascinating topic. This lecture covers the formula for determinants, the concept of cofactors, and their application to tridiagonal matrices.

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### Q: What is the formula for finding determinants of 2x2 matrices?

The formula for finding the determinant of a 2x2 matrix [a b; c d] is ad - bc.

### Q: What is the significance of finding determinants using the cofactor formula?

The cofactor formula allows for the determination of determinants of larger matrices by breaking them down into determinants of smaller matrices. This formula helps simplify the calculation process.

### Q: How can you determine if a matrix is singular using determinants?

If the determinant of a matrix is zero, the matrix is singular, meaning it does not have an inverse. This can be handy for identifying singular matrices.

### Q: How do you calculate the determinant of a tridiagonal matrix?

The determinant of a tridiagonal matrix can be calculated by applying the cofactor formula repeatedly, dividing the matrix into smaller sub-matrices until reaching 2x2 matrices, for which the determinants are easily calculated.

## Summary & Key Takeaways

• The lecture introduces the concept of determinants and their historical significance in linear algebra.

• The lecturer explains the formula for determinants and how it can be applied to find determinants of 2x2 and 3x3 matrices.

• The concept of cofactors is introduced as a way to break down the determinant formula for larger matrices.

• The lecturer provides examples of finding determinants using the cofactor formula for tridiagonal matrices.

• The periodic nature of the determinants for tridiagonal matrices is discussed.