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
Mat 252
SHOW ALL WORK
1.
3.
(Spts each) Compute each matrix given
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(Spts) Use technology to calculate A2 if A =
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f Mat252 Exam-1 Name i451
SHOW ALL WORK Date 02/18/2016
+ h = 2
1. (5 pts each) Choose the h and k such that the system has, 1:, x2
4xl + 8x2 2 k
a. Use row operation to solve
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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 304
Linear Algebra
Lecture 1:
Systems of linear equations.
Linear equation
The equation 2x + 3y = 6 is called linear
because its solution set is a straight line in R2 .
A solution of the equation is a pair of numbers
(, ) R2 such that 2 + 3 = 6.
For
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 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 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 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
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Mat 252
Sample Test-1
Notes
1.1: System of Linear Equations
1. Know how to solve a system of linear equations using elementary row operations.
2. Know the concept of consistent: (solution is unique compared to infinite) versus Inconsistent
3. Know how to