Question

Question 6 1 pts A 3x3 matrix with real entries can have (select ALL that apply) (Hint: If you consider characteristic polynomial of the matrix then this is an algebra problem) one real eigenvalue and two complex eigenvalues. two real eigenvalues and one complex eigenvalue. three eigenvalues, all of them real. three eigenvalues, all of them complex. only two eigenvalues, both of them real. only one eigenvalue -- a complex one. only two eigenvalues, both of them complex only one eigenvalue -- a real one.

Answer 1

given 1933x3 matoix with Meal entries - solution & 01 one real ergenvalue and two complex ergen volue. three degree so Explanation given matrix A has 3x3.. so Characte estic Polynomial always having polynomial. we known that have a stakement. every old degree polynomial having at least one meal root" Hence use this statement given polynomial is odd degree so . Porynomial having one heal eigen value and two complex eigen colue. all

eo g. A: 1 0 Characterstie polyo 07 Ars GCA). 23-1 GLADE D-1) (x 2 + x1) Henue this value of Ais eigen CT CAI =0 ㅋ Q-1) (1 24 14230 Xot. A r = 17 / 1-4 2 22 ) 2 472 1432 one meal eigen alue is complexo A have value ond Hence two eigen Uulue Beca use if 02 > two real eigenvalues and one complex eigen coluer Explaint Never possible A has three eigen value. theo real eigen volves never possible because complex eigen values always en conjugale pair le and one complex eigen value

if one complexo eigen volue ante positive then value Olways en paino possible. Other are Negative ergen so this is Not 03. three value all of them real eigen yes. Exploin eig A بلا L o 0 1 0 0 0 1 GCASE (-23 eigen value of Are Isl, 1 which 98 real 07 three Explain » eigen value all of them Complexo, not possible heason point on and point @ two volues / masix having OS Only eigen Both of them real. Explain - No Because given Order 3 X3. So Characterstic polyn nomial always three degree polynomial. 4 we known that three degree polynomial have always three roots.cer always obtained three eigen value which is only two eigen value is Not possible, volue a complex ona 06) Only One engen No, Reason (of similar Explain

Only two ergenvalues Both of them comples Explain Not possible. Reason. 05 simi 199 value a meal one only One . eigen Explain → Not possible Reason 5 similor Thanku