A 3x3 matrix A has characteristic polynomial p(lambda) = (lambda-2)(lambda-3)(la
ID: 3083708 • Letter: A
Question
A 3x3 matrix A has characteristic polynomial p(lambda) = (lambda-2)(lambda-3)(lambda+2). Give a diagonal matrix D that is simiar to A.Explanation / Answer
you have a matrix |1 |0 |-1 | |2 |3 |-1 | |0 |6 |4 | det(A- ?I) --> |1-?|0 |-1 | |2 |3-?|-1 |----> |0 |6 |4-?| det(A- ?I)=(1- ?)(3- ?)(- ?)+0+(-1)(2)(6)-0-(6)(-1)(-)(1- ?)-0 by working out the determinant of the 3*3 matrix A-lambda I to work out the determinant of a three by three matrix select any row or column. here lets choose row 1. then the determinamt is (1-?)* determinant of the 2*2 matrix not covered by the row or column thats in - 0 * the 2*2 matrix ....... + -1* determinat of the 2*2 matrix ...... it doesnt matter which row or column you pick you get the same answer. and the determinant of a 2*2 matrix is ad-bc