© Zarestky
Math 141 Week in Review
Week 2 Key Topics
Section 1.5
•
•
Write the least-squares or linear regression line by using LinReg on your calculator.
Correlation coefficient r
o Measures how close the data points are to the line.
o The closer the value is to ±1, the better the line fits the data. If the value is
near 0, the data is not really linear.
Section 2.1
•
•
Solve a system of linear equations. There are three possible outcomes:
o Exactly One Solution
 The graphs of the two lines intersect in exactly one point.
o No Solution
 The graphs of the lines do not intersect.
 The lines are parallel: same slope, different y-intercepts
o Infinitely Many Solutions
 The two lines are the same: same slope, same y-intercept
 The graphs of the lines overlap.
 The solution is always parametric.
Set up a system of linear equations.
o Define all variables, including units.
© Zarestky
Math 141 Week in Review
Sections 2.2-2.3
•
•
•
Convert between augmented matrices and systems of equations.
A matrix with m rows and n columns is of size m × n.
Perform Gauss-Jordan elimination. There are three allowable operations:
o Interchange any two rows. Notation: Ri ! R j
o Multiply a row by a constant. Notation: cRi ! Ri
o Add a multiple of one row to another row. Notation: cRi + R j ! R j
•
Identify the row-reduced form of an augmented matrix. (aka reduced row echelon)
o The result of Gauss-Jordan elimination.
o The first nonzero entry in each row is a 1, called the leading 1.
o In any two successive nonzero rows, the leading 1 in the upper row is left of
the leading 1 in the lower row (stair-stepped top-left to bottom-right).
o If a column contains a leading 1, then all other entries in that column are zeros.
o If a row contains only zeros, it moves below all other rows with nonzero entries.
Find solutions from a row-reduced matrix.
o If there is a row containing all zeros to the left of the vertical line and a
nonzero entry to the right of the line, then the system has no solution.
o If the above is not true and if not all columns left of the vertical line contain a
leading one, then there are infinitely many solutions. Make the columns
without leading 1’s your parameters and write the parametric solution.
•