1. The problem statement, all variables and given/known data Let A be the matrix with eigenvalues x1 = 2, x2 = 1, x3 = 1/2 , x4 = 10 and corresponding eigenvectors v1: <1,-1,1,0>, v2: <1,-1,0,0>, v3: <1,0,0,1>, v4: <0,0,1,1> Calculate |A| 2. Relevant equations See above 3. The attempt at a solution I'm not really sure how to start this problem but i know that: For nxn matrices X, Y , Z |XYZ| = |X| |Y| |Z| and |X^ (-1)|= 1 / |X| Maybe I could use this to solve the problem? Any input or suggestions about how to start this problem would be helpful! Thanks!:)
What does the matrix of your linear transformation look like if you express it in the basis {v1,v2,v3,v4}?
Do you know the relationship between the eigenvalues of a matrix and the determinant of that matrix? It is a standard result. If it is not in your textbook or course notes, it can certainly be found through Google. RGV