Learning about matrices is incomplete without learning about Determinants. The determinant of a Matrix is computed by all the elements of that matrix. The existence of inverse of a matrix is directly dependent upon the value of its determinant. It is a very useful concept in Algebra. Let’s study more in the topics below.
- Determinant of a Matrix
- Properties of Determinants
- Minors and Cofactors of Determinant
- Area of a Triangle Using Determinants
- Adjoint and Inverse of a Matrix
- Solution of System of Linear Equations using Inverse of a Matrix
FAQs on Determinants
Question 1: What is the use of determinants?
Answer: We use determinants for solving linear equations, it captures how linear transformation change area or volume, and for changing variables in integrals. Moreover, we can see determinants as a function whose input is a square and output is a number.
Question 2: What does it mean if a determinant is 1?
Answer: Generally, determinants are defined only for square matrices. Furthermore, if a determinant of a matrix is 0 then the matrix is said to be singular, on the other hand, if the determinant is 1 then it means the matrix is unimodular.
Question 3: Why do we study determinants?
Answer: Simply, the determinants of a matrix refer to a useful tool. As the name suggests, it ‘determines’ things. In addition, while doing matrix algebra, or linear algebra, the determinant allows you to determine whether a system of equations has a unique solution or not.
Question 4: Can determinant be negative?
Answer: A determinant is a real number and it is not a matrix. Furthermore, it can be a negative number. Also, it is not related to absolute value at all except the fact that they both use vertical lines.