Summary: Mathematics 3C Summer 3B 2009
Worksheet 9, September 8th, TA Grace Kennedy
PREP for 9/10: Finish worksheets, and STUDY STUDY STUDY!
MY WEBSITE: http://math.ucsb.edu/kgracekennedy/SB093C.html
Write clearly and justify every step. Consider the following system of linear
x1 +2x2 +x3 +2x4 +3x5 = 0,
x1 +2x2 +2x3 +3x4 +4x5 = 0,
2x1 +4x2 +2x3 +4x4 +6x5 = 0.
1. Write out the coefficient matrix this homogeneous system of linear equa-
2. Use the elementary row operations to put the matrix in row-reduced ech-
3. Find a basis for the row space W R5
of the coefficient matrix, the
subspace of R5
spanned by the rows of the original matrix. What is the
dimension of W?
4. Find a basis for the space W