Math 225 Midterm One Exam Questions And Well Elaborated Answers 100% Guaranteed.

Finding a parametric description of the solution set of a linear system is the same as solving the system. Is this statement true or false? - correct answer The statement is false. The solution set of a linear system can only be expressed using a parametric description if the system has at least one solution. If one row in an echelon form of an augmented matrix is [ 0 0 0 5 0 ] then the associated linear system is inconsistent. Is this statement true or false? - correct answer The statement is false. The indicated row corresponds to the equation 5x4 = 0, which does not by itself make the system inconsistent. Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. - correct answer The system is consistent because the rightmost column of the augmented matrix is not a pivot column. Suppose a 6x8 coefficient matrix for a system has six pivot columns. Is the system consistent? Why or why not? - correct answer There is a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have a row of the form [ 0 0 0 0 0 0 0 0 1 ] so the system is consistent. A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Can such a system have a unique solution? Explain. Choose the correct answer below. - correct answer No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution. What is the geometric relationship between u, -v, and u-v? - correct answer he vectors u, -v, and u-v form a parallelogram whose other vertex is at 0. When u and v are nonzero vectors, Span{u,v} contains only the line through u and the line through v and the origin. - correct answer False. Span{u,v} includes linear combinations of both u and v. Any list of five real numbers is a vector in set of R5. (Real Numbers). - correct answer True. set of real numbers R Superscript 5 denotes the collection of all lists of five real numbers. If A is an mxn matrix, then the columns of A are linearly independent if and only if A has _______ pivot columns. - correct answer n pivot columns