Question

2 invertible? C For which values of c is the matrix 8 O c 4 c =-4 Both of the above, i.e., c +4 Neither of the above, i.e., c +4. Suppose that the following row operations: interchange rows 1 and 3 multiply row 3 by 1/2 add -3 times row 1 to row 2 2 1 7 in this order, transform a matrix A into B = | 0 4-5 L0 0 3 What is the determinant of A? -48 -12 48 12 Suppose that A is an nxn matrix. Which of the following statements is FALSE? If det (A) 0. then A is invertible. d (det(A)) det(A2) det (2A) 2 det(A) If det (A) 0, then the columns of A are linearly dependent.

Answer 1

is inventi ble then 60 C 2 CY-8 (2) 0 #0 C ○キ 91-2 91キ う C+±4 60 for the both c 4 and C - 4, the qiven maGux becomes ioventible 2) clet CB) where BPs obtauned as 2C4) (3)=24 Tn ter changing rows 1and 3 in A Multiply roo 3 by add -3 thimes rouo to Yow2 -48 E(2) detCB) So that dlet CA) True 3) If det CA) 0 then A is invertible TYue clet CA A) det CA). dlet (A) -det CA)) clet CA) =2 detCA) Falsel Sin ca det (2A) = 2 det CA) clet C2A) uinearly Lf det CA) 0 then tre columns of A coe TRUR dependent