Question

IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the inverse of AB equation Ai has at least one solution. where vh is any solution of the equation Ax = 0 and p is a solution of Ai the trivial solution. 1Q 10. (10) Determine if the following are True or False. a) Two matrices are row equivalent if they have the same number of rows. b) The reduced echelon form of a matrix is unique c) The weights c1, c2, ..., Cp on a linear combination cvi+ +cpop cannot all be zero. d) If the equation A-b is consistent then b is in the span of the columns of A e) A linear transformation preserves the operations of vector addition and scalar multiplication

Answer 1

OF them can be obtained from other operation ng elementa ry-ro Both of the matrices A and B have nun loer.-0 e_rovvs butーno ne oe--the matrix can be obtained from other by elementary rovw operations this is a False statement . True.(caforproveto爿atrinduet i on method o- for nx m matrix span [ujv contains all vectors C This is false. The of the form cutov丿ceR-These vector form a tine through u and origin ALSO beth caiso can be o, to be totatly independent

e) True (By definition of linear Tvansjormation d Let consider the system AX B a 1 an amn_」 Lami ama since the system is consistent, 3 x : X1 such that Ax E B X2 in a 21 amn a mi Non. AX = B aan 0 12 a 21 a mn a mi R is the linear span of columns of A