- #1
isa_vita
- 3
- 0
A is a square matrix n*n with the following properties: A*A=A and A not equal I (identity matrix).
How to prove the following equation:
(I+A)^-1=I+A/2 ?
How to prove the following equation:
(I+A)^-1=I+A/2 ?
That's exactly what I did- and did NOT get the identity matrix.chiro said:Assuming that the inverse even exists why not just multiply both sides by (I + A) and collect terms? (Remember I'm assuming that the inverse of this exists which it may not, since I haven't checked it).
Linear algebra is a branch of mathematics that deals with the study of vectors, matrices, and linear transformations. It involves solving equations and manipulating mathematical objects to understand and solve problems related to linear systems.
Linear algebra is a fundamental tool used in various fields of science, such as physics, engineering, computer science, and economics. It helps in solving complex problems involving multiple variables and has applications in areas like data analysis, machine learning, and computer graphics.
The basic concepts in linear algebra include vectors, matrices, linear transformations, eigenvalues and eigenvectors, determinants, and systems of linear equations. These concepts form the building blocks for more advanced topics in linear algebra.
Linear algebra is used in data analysis to manipulate and analyze large datasets. Matrices and vectors are used to represent and store data, while operations like matrix multiplication and eigenvalue decomposition are used to perform computations and extract valuable insights from the data.
Linear algebra has numerous real-world applications, such as image and signal processing, robotics, computer graphics, cryptography, and optimization problems. It is also used in fields like physics, statistics, and economics to model and solve various problems.