Question

the last pic is number 14 please answer it as a,b,c,d as well.

thanks

1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1 c) k = 2 d) all of the above 4. if O is an eigenvalue of matrix A, then the set of columns of A is linearly independent? a) False b) The statement is incomplete c) True d) None of the above 5. The span of any finite set of vectors in a vector space is closed. a) Under subtraction and scalar multiplication b) Under addition and scalar multiplication c) Under addition and subtractions d) None of the above 6. There is a set of 9 linear independent vectors then the dimension is a) RS b) R12 c) RS d) All of the above 7. If A is an nxn matrix, then which of the following statements are equivalent a) All of the above b) A is invertible c) A has a rank n d) det(A) # to 0

Answer 1

14 APO i § 11 To 12 eigenvalues of marrin I are A-il zo 12-1 0 I and lao loi 1 24 (2-1){(2-1)°4)-63-4) zo (4-2)[04-2) ?-1-1) = 0 (-a) (x?-41+4-2=0 (4-2) 442-44 +2)=0 As 2,248 option 6) 2+2, 2-3,2