UNIVERSITY OF TORONTO
DEPARTMENT OF STATISTICAL SCIENCES
STA247HlS-Probability with Computer Applications
Time: 90 Minutes
Midterm Exam A
1. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SI
MAT224 Assignment 2 - SOLUTIONS
Due Tuesday Oct 13 at the beginning of the lecture
1. In each part, a linear map (also called a linear transformation) between two vector spaces is given, together with a basis of the domain and a basis of the target. Find
An Example for 1.6
Question: Find a basis for the subspace
W := cfw_f(x) 2 P4 (R) : f(1) = f 0 (1) = 0
of P4 (R).
Solution: Consider a polynomial
f(x) = a4 x4 + a3 x3 + a2 x2 + a1 x + a0 .
It is easy to see that
f(1) = a4 + a3 + a2 + a1 + a0
MAT224 Test 1 Information and Review Sheet
Time and Date: Regular sitting: Friday October 23 12-2
Early sitting: Same day 10-12
If you wish to write the early sitting, send your instructor an email as soon as possible.
Location: You will be divided into s