Math 108: Final Exam, Fall 2017 2/ 10 1. Consider the following matrices: 0 1 1 2 1:1:[752 $],B=[g j,0= 2 3,1):32 3 1 1 0 Evaluate, if possible, If not possible, give reason(s). (a) (5 points) 3A + ZBC (b) (5 points) DBA (c) (5 points) 303+ 101T (d) (5 points) ((30,254 Math 108: Final Exam, Fall 2017 3/ 10 2. (10 points) For what value of k, if any, Will the system have (a) no solution, (b) a unique solution, (c) innitely many solutions. :9 + Icy : 1 km + y : 1 3. (5 points) Let A be an idempotent matrix, meaning A2 : A. Find all possible values of det(A). Math 108: Final Exam, Fall 2017 4/ 10 1 1 1 1 4. (10 points) Determine if these vectors for a basis for R3: 1 , 2 , and 3 . If so, write *2 as a 1 3 6 3 linear combination of these vectors. 932 5- (5 points) Let S : {[31] $2 is even}. Is S a subspace of R2? Justify your answer. Math 108: Final Exam, Fall 2017 5/ 10 6. Consider the matrix 0 1 1 A : 1 2 O 1 3 2 (a) (13 points) Find the inverse of A. 1 (b) (2 points) Solve the following system of equations: As? : 2 Math 108: Final Exam, Fall 2017 6/ 10 7. (10 points) For the matrix 0 1 2 3 4 A = 0 2 0 3 5 7 4 0 6 9 12 7 10 with reduced row echelon form, [0 1 0 -1 0 0 01 2 0 0 0 0 0 1 0 0 0 0 0 find a basis for the the column space and the null space of A