Determinants: Understanding Their Significance in Matrices

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

1

Academic year

2022
Author

Sporkz
Views

30

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:Arial;color:#000000;} .ft02{font-size:18px;font-family:ArialMT;color:#000000;} .ft03{font-size:18px;line-height:22px;font-family:Arial;color:#000000;} .ft04{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} More Determinants Determinant is a type of function that can be used to determine the value of an element ina given matrix. The determinant is a single number that can be used to determine whethera matrix is invertible or not. Now, we need to define some terminology, so let's say that A is equal to--well, what is it?Well, the definition of this will be that this quantity is equal to 1 times the determinant ofwhat you get by looking in this lower right corner. And the 2 by 2 determinant-- b2, b3, c2, c3. Then you subtract a2 times the determinant ofb1, b3, c1, c3. Then you will multiply the determinant by 3 and take a3 times b1, b2, c1, and c2. Each ofthese terms means that you multiply b2 by c3 and subtract c2 times b3 from this product,then subtract this product from that one, and so on. So there are actually six terms in the 3 x 3 determinant formula. Some of you may haveseen a different formula for 3 x 3 determinants that lists six terms. It is the same definition;they are one and the same.