Mark each statement true or false. justify each answer. a. a homogeneous system of equations can be inconsistent. choose the correct answer below. o a. true. a homogeneous equation can be written in the form ax o, where a is an mxn matrix and 0 is the zero vector in r". such a system ax -0 always has at least one solution, namely x-0. thus, a homogeneous system of o b. true. a homogeneous equation cannot be written in the form ax 0, where a is an mxn matrix and o is the zero vector in r. such a system ax 0 does not have the sclution x 0. thus, a homogeneous system of equations can be o c. false. a homogeneous equation cannot be written in the form ax-0, where a is an mxn matrik and o is the zero vector in , such a system ax 0 does not have the solution x 0. thus, a homogeneous system of equations cannot equations can be inconsistent inconsistent. d. fa se. a homogeneous equation can be w en n the form ax-0, where a is an m x n matrix and。เร the zero vector in such a syster b. if x is a nontrivial solution of ax 0, then every entry in x is nonzero. choose the correct answer below. o a. true. a nontrivial solution of ax o is a nonzero vector x that satisfies ax 0. thus, a nontrivial solution x cannot have any zero entries ax: o always has atleast ne solution, namely r- . us, a homogeneous system of equations cannot be inconsistent. b. falso. a nontrivial solution o, ax-ο is a nonzero vector x that satisfies ax 0. thus, a non ri ial solution x can have some zoro en ries so long as not all of its o tries are zero. true. a nontrivial solution o ax-o is a nonzero vector x hat satisfies ax=0. thus, a non rval solution x can have some zero entres so long as not all of its entries are zero. false. a nontrivial solution of ax = 0 is the zero vector. thus, a nontrivial solution x must have all zero entries. o c d. c. the effect of adding p to a vector is to move the vector in a direction parallel to p. choose the correct answer below. oa. false. given v and p in r2 or r3, the effect of adding p to v is to move v in a direction parallel to the plane through p and o o b. false. given v and p in r2 or r3, the effect of adding p to v is to move v in a direction parallel to the line through v and 0 o c. false. given v and p in r2or r3, he effect of adding p to v is to move v in a direction parallel to the plane through v and o d. true. given v and p in r2or r3 the effect of adding p to v is to move v in a direction parallel to the line through p and 10 d. the equation ax- b is homogeneous if the zero vector is a solution. choose the correct answer below. a. false, system o linear equations said to be homogeneous it can be written in the or m ax-o where aisan men matrix and 0 s the zero vector in r the zero ector sa so ution, th n x a 0 nic s alse b true. a s stem o linear equations is said to be homo eneous r t can be written in the orm ax·0, w ere a s ar m n matrix a dos ezero vector in r rthez o vector sa so on, then b- eao o c. false. a system o linear equations is said to be homogeneous t can be written in the orm ax = b, where a is an m x n matrix and b is a nonzero vector i r thus, the zero vector is never a solution o a homogeneous s stem. od. true. a system of linear equations is said to be homogeneous if it can be written in the form a b, where a is an mxn matrix and b is a nonzero vector in rm. if the zero vector is a solution, then b o e. if ax = b is consistent, then the solution set of ax = b is obtained by translating the solution set of ax = 0-choose the correct answer below. o a. true. suppose the equation ax bis consistent for some given b. then the solution set of ax- b is the set of all vectors ofthe form w-pth, where v, is not a solution of the homogeneous equation ax-0. ob. true. suppose the equation ax b is consistent for some given b, and let p be a solution. then the solution set of ax b is the set of all vectors of the form w ptn, where v, is any solution of the homogeneous equation ax c. false. suppose the equation ax b is consistent for some given b. then the solution set of ax -b is the set of all vectors of the form w ptvh, where vh is not a solution of the homogeneous equation axo o d false. suppose the equation a = b s consistent or some given b, and let p be a solution. then the solution set o agz b is he set o an vectors o the orm w--vh where h і any solution o the homogeneous equation ax-0.