MATH 221 Midterm: MATH 221 2005 Winter Test 1

• School: UBC
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

If you use more than one booklet, put your name and the number of booklets used on each booklet. Show enough of your work to justify your answers: (15 points) consider the system of equations. 2x + (2 + q)y + 3z = 1, y. 2y where the constant q is not speci ed. Remember to provide some calculations and/or other reasons to support your answers: (10 points) consider the following transformations on r2. Then re ect the result of the rst step in the x1-axis. Show that combining these two steps has the same e ect as simply re ecting each input vector in a suitable line, and nd that line: (15 points) let w be the subspace of r3 spanned by the vectors. Do the following three things in some order, and then answer the fourth part. (a) find a basis for w and nd the dimension of w . (b) determine whether the vector ~v = .