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Andrew Jason Linear algebra is perhaps the most powerful and useful math course you can ever take in your entire academic career. Resting at the heart of this course is something called a matrix. A matrix is a rectangular array of numbers organized in rows and columns and encased in brackets.
Matrices are very useful due to the fact that they can be easily manipulated. In this page we will explore how to find the inverse of a matrix and its uses. Much like normal numbers we use the notation A -1 to denote the inverse of matrix A.
Some important things to remember about inverse matrices is they are not commutative, and a full generalization is possible only if the matrices you are using a square. An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. A matrix is said to be a singular matrix if it is non-invertible.
A matrix is a nonsingular matrix if it is an invertible matrix. A simple formula for finding the inverse of a 2 x 2 matrix is given by Theorem 4: We call the quantity ad - bc the determinant of the matrix.
Theorem 5 reveals something else useful about the inverse of matrices. The following example demonstrates this usefulness of this equation. The following proof will help prove theorem 5 by proving 1 that the solution exists and 2 this solution is unique.Here is the solution of our previous blog about the German Accusative Case 🙂.
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