Finding a Matrix GIVEN it's Eigenspaces [Passing Linear Algebra]

Method 1: 0:21
Method 2: 3:36

[@ngonidzashekimbini7177]

thank you

[@admel8933]

how do you know that 1 and -2 are the eigenvalues? is it just because they are given?

[@stemsupport3645]

Yes they are given. The eigenspaces are labeled as the 1-eigenspace and the -2-eigenspace. Therefore, if a vector is in the 1-eigenspace (if it lies on the line labeled 1-eigenspace) it is an eigenvector with eigenvalue 1, and if a vector is in the -2-eigenspace it is an eigenvector with eigenvalue -2.