Math 221 Exam Questions with 100% Correct Answers

What is a matrix of coefficients? Correct Answer The matrix formed of all the coefficients of one or more sums of variables with coefficients. What is an augmented matrix? Correct Answer The matrix formed of all the coefficients and values of one or more linear equations. What is row echelon form? Correct Answer When each leading entry is to the right of those above it, and any rows of zeros are at the bottom. What is reduced row echelon form? Correct Answer When all leading entries are 1 and each column containing a leading entry has only zeros elsewhere. What is a row reduction procedure? Correct Answer Multiplication, division, addition or subtraction between rows in a matrix How do you solve a system of linear equations? Correct Answer Perform row reduction procedures until the matrix is in reduced row echelon form. What is a pivot? Correct Answer The location of a leading entry. What is a pivot column? Correct Answer The column in which a pivot is located. What is a free variable? Correct Answer A variable in a non-pivot column for which there isn't a single defined value. What is a basic variable? Correct Answer A variable in a pivot column for which there is a single defined value. What is a consistent system of linear equations? Correct Answer A system that has at least one solution. How do you check if a system of linear equations is consistent? Correct Answer Stick 'em in a matrix and solve 'em! If there is a pivot in the last column, it's consistent. What is the span of some set of vectors? Correct Answer The set of all linear combinations of the vectors How do you check if a vector is in the span of some set of vectors? Correct Answer Set that vector as the solution to the others, stick it all in a matrix, and solve for consistency. How do you check if a span of some set of vectors in R(m) is all of R(m)? Correct Answer Check if the vectors can be scalar multiplied to cover R