Summary: MAT 307 FALL 2011 MIDTERM I EXAM
Name: ID Number:
Problem 1 2 3 4 5 6 Total
Directions: Each problem is 15 points; some problems are easier, some harder. Do all of your
work on these pages and cross out any work that should be ignored. Use the backs of pages if
needed, indicating where you've done this. Notes, books, calculators and discussions with others
are not permitted.
1. Find the equation of the plane in R3 through the 3 points (1, 0, 0), (2, 1, 1), (1, 2, 3).
2. Consider the linear system
x + y + z = 1
x - y = 1
x + y = 2
a. Write this system in matrix form A · x = b.
b. Find the row-reduced form of this linear system
c. Find all solutions of the linear system and describe the solution set.
a. Find all real numbers a for which the matrix