Math 215: Assignment 10
This assignment is not to be handed in. You should still complete this assignment, as you
will most certainly nd problems like some of these on your nal exam.
2
1
1. Find by pr
MATH 215: Assignment 7
Due Thursday November 8, 2012 IN CLASS (at 9:30am)
1. Determine whether the following sets are linearly independent.
(a) A = cfw_3 2x + x2 , 2 5x + 2x2 , 6 + 7x 2x2
(b) B =
1 0
MATH 215: Assignment 6
Due Thursday November 1, 2012 IN CLASS (at 9:30am)
1. Invent a 2 2 matrix A that has eigenvalues 1 = 2 and 2 = 3 with corresponding eigen1
1
vectors v1 =
and v2 =
2
3
2. Find th
MATH 215: Assignment 8
Due Thursday November 15, 2012 IN CLASS (at 9:30am)
1. Determine whether cfw_1 +
x2
,1
2
x2
,x
2
+
x3
,x
6
x3
6
is linearly independent in P4 .
2. Suppose that S = cfw_x, y, z
MATH 215: Assignment 9
Due Thursday November 22, 2012 IN CLASS (at 9:30am)
0
3
2 , 2 is a basis for the plane 2x1 3x2 +2x3 = 0. (Hint: To check
1. (a) Verify that B =
0
3
whether the set spans th
MATH 215: Assignment 2
Due September 27, 2012 IN CLASS
1. Calculate the area of the parallelogram determined by the vectors.
3
4
(a) 1 and 2
1
3
3
4
3
4
1 and 5 in R3
(b)
and
Hint: Consider t
MATH 215: Assignment 3 SOLUTIONS
1. For each of the following homogeneous systems:
(a) Write the coecient matrix
(b) Determine the rank and the number of parameters in the general solution
x1 + 5x2 3x
MATH 215: Assignment 1 Solutions
1. (a) Find all the solutions, including complex solutions, of the equation z 6 1 = 0. Plot
these solutions in the complex plane.
Solution:
2nj
We think of 1 as e2nj f
MATH 215: Assignment 5 SOLUTIONS
1. Determine all values of p such that the matrix is invertible.
p 0
0
p
(a) R = p2 2
p 8 p 1
Solution: Recall that in order for a matrix to be invertible, det R = 0.
+1 for angle A
+1 for B
+1 for C
+1 for AB x
AC
+1 for area
+1 first step
+1 second step
+1 for
parametrisation
+1 for backwards
substitution
+1 for the correct general solution
Maximal scores for P.3
MATH 215: Assignment 5
Due Thursday October 18, 2012 IN CLASS (at 9:30am)
1. Determine all values of p such that the matrix is invertible.
p 0
0
p
(a) R = p2 2
p 8 p 1
1 1 1
(b) T = 2 p p
2 2 1
2. I
MATH 215: Assignment 4
Due Thursday October 11, 2012 IN CLASS (at 9:30am)
1. Evaluate the determinants of the following matrices.
2
3
1
2 5
(a) A = 4
0 3
0
4 0 0
(b) B = 11 3 0
15 17 8
2. A matrix i
MATH 215: Assignment 3
Due Thursday October 4, 2012 IN CLASS
1. For each of the following homogeneous systems:
(a) Write the coecient matrix
(b) Determine the rank and the number of parameters in the
Math 215: Assignment 2
due Friday, October 2, 4:00 pm
1. Let L be the line and let P be the plane in R3 , represented by the equations
1
4
L : p = 0 + t 2 , t R,
P : x + 3y + 2z = 9,
1
3
respectively.
Math 215: Assignment 3
due Friday, October 9, 5:00 pm
1. Solve the system of equations by reducing the augmented matrix to the RREF and write
down the general solution to the SLE represented by that R
Math 215: Assignment 7
due Friday, November 13, 5:00 pm
1. For each vector space below, find a basis for that space and state the spaces dimension.
a)
V =
v
w
x
y
z
v
4v
R5 : 5v
2v
3v
+ w 2x
3w +
Math 215: Assignment 5
due Friday, October 23, 5:00 pm
1.
a) Compute the rank of the matrix:
3
4 8 10
6
1 7 9
A=
12 5 5 7 .
6 13 11 19
b) Suppose B is a 6 9 matrix of rank 4. How many leading varia
P1 and P7 are to be marked throughly, other Ps - for the presence of the
correct answer & solution only
+1
+1
+1
+2
Max +5 for P1
Answer +0.5
Counterexample +0.5
Answer +0.5
Proof +0.5
Answer +0.5
Pro
Math 215: Assignment 1
due Friday, September 25, 4:00pm
1. Let z = 3 2j. Find the standard form of the complex numbers:
a) z
b) |z|
c) arg(z)
d)
2z 2
z+j
2. Find the polar and exponential forms of the
P1 and P3 to mark throughly, rest - for completeness
+1 = 0.5 for REF +
0.5 for rank
+1 for rank(B)=rank(B^T)
+1 for answer
+1 for x = p + h
MAX +5 pts for P1
+1 for conclusion
Each part a) b) c) d) e
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
+0.5
max +5.5 for P1
P1 and P7 to mark throughly according to scheme
rest - for completeness (+2 points max each)
+0.5 for equation
+0.5
+0.5 for each
Math 215: Assignment 6
due Friday, November 6, 5:00 pm
1. Determine if a given set V together with the addition and scaling operations is a
vector space over the field of real numbers R:
a
a
c
a
MATH 215: Assignment 1
Due September 20, 2012 IN CLASS
1. (a) Find all the solutions, including complex solutions, of the equation z 6 1 = 0. Plot
these solutions in the complex plane.
(b) Draw the un
MATH 215: Assignment 2
Due September 27, 2012 IN CLASS
1. Calculate the area of the parallelogram determined by the vectors.
3
4
(a) 1 and 2
1
3
3
4
3
4
1 and 5 in R3
(b)
and
Hint: Consider t