Question

Select True or False. No work is required. Let A= [o 1 2 0 4 and y = [6 3]. lil 1. True or False: The Eigenvalues of A are -1 and 4. 3 2. True or False: is an Eigenvector of A. 1 3. True or False: The columns of A are linearly independent. 4. True or False: The columns of A form a basis for R2. 5. True or False: The rank of A is 3. 6. True or False: The nullity of Ais 0. 7. True or False: The characteristic polynomial of Ais 12 – 31 – 4. 8. True or False: A2 – 3A – 41 is the zero matrix. 9. True or False:y is orthogonal to the first row of A. 10. True or False: Ay is undefined. 11. True or False: A is singular. 12. True or False: y is a unit vector.

Answer 1

Given that, A = =[ 0 2] § ya qy=[8] ♡ True. Since, diagonal entries are eigenvalues for diagonal matrix False If y is eigenvector then av is also eigenllector Here. AVZav. in. Avtal or AVI 47. True" Since, det CA) to 4 True! since columns are linearly independent false! As rank CA)=2 True! Because A is invertible matrix true Since, det Cau-A) = 2²-32-4 True Every matrix satisfies it's characteristic polynomial. @ false since (a). 6+ 0.3 to false: Ay is defined. & Ay= [ ; 12 W false As det CA) to fake since, llyll 1