You are watching: A homogeneous system of equations can be inconsistent. choose the correct answer below.
Transcribed image text: a. A homogeneous system of equations have the right to be inconsistent. Pick the exactly answer below. O A. False. A homogeneous equation can be written in the form Ax = 0, whereby A is an mxn matrix and also 0 is the zero vector in Rm. Such a device Ax = 0 constantly has at the very least one solution, namely x= 0. Thus, a homogeneous mechanism of equations can not be inconsistent. B. False. A homogeneous equation can not be written in the form Ax = 0, where A is one mxn matrix and also 0 is the zero vector in Rm. Together a system Ax = 0 does not have actually the equipment x = 0. Thus, a homogeneous mechanism of equations cannot be inconsistent. O C. True. A homogeneous equation deserve to be created in the form Ax = 0, where A is an mxn matrix and also 0 is the zero vector in Rm. Together a mechanism Ax = 0 constantly has at the very least one solution, specific x = 0. Thus, a homogeneous device of equations can be inconsistent. D. True. A homogeneous equation cannot be written in the type Ax = 0, wherein A is an mxn matrix and O is the zero vector in Rm. Together a device Ax = 0 walk not have actually the systems x = 0. Thus, a homogeneous system of equations have the right to be inconsistent. B. If x is a nontrivial equipment of Ax = 0, then every entrance in x is nonzero. Choose the correct answer below. O A. True. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not every one of its entries room zero. B. False. A nontrivial equipment of Ax = 0 is the zero vector. Thus, a nontrivial solution x must have all zero entries. C. True. A nontrivial systems of Ax = 0 is a nonzero vector x the satisfies Ax = 0. Thus, a nontrivial equipment x can not have any kind of zero entries. D. False. A nontrivial solution of Ax = 0 is a nonzero vector x the satisfies Ax = 0. Thus, a nontrivial solution x have the right to have some zero entries so lengthy as not all of its entries room zero. C. The result of including p come a vector is to relocate the vector in a direction parallel to p. Pick the correct answer below. A. True. Offered v and p in R2 or R3, the result of adding p to v is to relocate v in a direction parallel come the line through p and 0. B. False. Offered v and p in R2 or R3, the result of adding p come v is to move v in a direction parallel to the airplane through p and 0. C. False. Provided v and also p in R2 or R3, the result of adding p to v is to relocate v in a direction parallel come the line through v and also 0. OD. False. Given v and p in R2 or R3, the result of adding p come v is to relocate v in a direction parallel to the plane through v and also 0. D. The equation Ax = b is homogeneous if the zero vector is a solution. Select the exactly answer below. O A. True. A device of linear equations is claimed to it is in homogeneous if it deserve to be composed in the form Ax=b, wherein A is one mxn matrix and also b is a nonzero vector in Rm. If the zero vector is a solution, then b= 0. O B. False. A device of linear equations is claimed to it is in homogeneous if it have the right to be created in the form Ax = b, whereby A is an mxn matrix and also b is a nonzero vector in RM. Thus, the zero vector is never a equipment of a homogeneous system. O C. False. A system of straight equations is stated to be homogeneous if it can be created in the kind Ax = 0, whereby A is one mxn matrix and 0 is the zero vector in Rm. If the zero vector is a solution, climate b = Ax = A0 = 0, i beg your pardon is false. O D. True. A system of straight equations is claimed to be homogeneous if it deserve to be written in the kind Ax = 0, where A is an mxn matrix and 0 is the zero vector in R™. If the zero vector is a solution, then b = Ax = A0 = 0. E. If Ax = b is consistent, climate the solution set of Ax=b is derived by translating the solution set of Ax = 0. Choose the correct answer below. A. True. Expect the equation Ax=b is continuous for some provided b, and let p be a solution. Then the solution set of Ax=b is the set of every vectors of the type w=p+Vh whereby Vh is any solution of the homogeneous equation Ax = 0. B. False. Suppose the equation Ax = b is consistent for some offered b, and let p be a solution. Climate the solution set of Ax=b is the collection of all vectors that the kind where Vh is any solution of the homogeneous equation Ax = 0. W=p+Vni C. False. Intend the equation Ax = b is regular for some offered b. Climate the solution collection of Ax = b is the collection of all vectors the the type w=p+V; whereby Vh is no a systems of the homogeneous equation Ax = 0. OD. True. Expect the equation Ax = b is continuous for some provided b.
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Then the solution set of Ax = b is the set of all vectors that the type w=p+V; wherein : Vh is no a solution of the homogeneous equation Ax = 0.