MATH 304502/506
Fall 2011
Sample problems for Test 2: Solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 (15 pts.) Let M2,2 (R) denote the vector space of 2 2 matrices with real
entries. Consider a linear operator L : M2,2 (R) M2
MATH 304502/506
Fall 2011
Sample problems for Test 2
Any problem may be altered or replaced by a dierent one!
Problem 1 (15 pts.) Let M2,2 (R) denote the vector space of 2 2 matrices with real
entries. Consider a linear operator L : M2,2 (R) M2,2 (R) give
MATH 304502/506
Fall 2011
Sample problems for Test 1: Solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 (15 pts.)
and p(3) = 7.
Find a quadratic polynomial p(x) such that p(1) = 1, p(2) = 3,
Let p(x) = ax2 + bx + c. Then p(1) =
MATH 304502/506
Fall 2011
Sample problems for Test 1
Any problem may be altered or replaced by a dierent one!
Problem 1 (15 pts.)
and p(3) = 7.
Find a quadratic polynomial p(x) such that p(1) = 1, p(2) = 3,
1 2
4
2
3
2
Problem 2 (25 pts.) Let A =
2
0 1
2
MATH 304502/506
Fall 2011
Sample problems for the nal exam: Solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 (15 pts.) Find a quadratic polynomial p(x) such that p(1) = p(3) = 6 and
p (2) = p(1).
Let p(x) = ax2 + bx + c. Then p
MATH 304502/506
Fall 2011
Sample problems for the nal exam
Any problem may be altered or replaced by a dierent one!
Problem 1 (15 pts.) Find a quadratic polynomial p(x) such that p(1) = p(3) = 6 and
p (2) = p(1).
Problem 2 (20 pts.) Let v1 = (1, 1, 1), v2
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