MAT 272 Linear Algebra
Additional Subspace problems. On Nov. 17 there will be an in-class quiz in which you will be
required to prove one of the following completely and accurately. In each problem the letters a,
b and c represent real numbers
1) Prove th
Beta
0.87
Number of Contracts
Rounded
Index now
Index Level in Two Months
Return on Index in Two Months
Return on Index incl divs
Excess Return on Index
Excess Return on Portfolio
Return on Portfolio
Portfolio Gain
Futures Now
Futures in Two Months
Gain o
MAT 272 Assignment #6
Due: Dec. 10, 2009
1) Let V be a vector space with basis . Let x,y V with coordinates relative to B of cfw_c1,c2,
, cn and cfw_d1, d2, dn respectively.
a. Find coordinates for x + y and kx relative to B.
b. Are your coordinates uniqu
MAT 272 Assignment #6 - solutions
Due: Dec. 10, 2009
1) Let V be a vector space with basis
. Let x,y
relative to B of cfw_c1,c2, , cn and cfw_d1, d2, dn respectively.
a. Find coordinates for x + y and kx relative to B.
and
V with coordinates
so
and
Simila
MAT 272 Assignment #6 - solutiuons
Due: Dec. 10, 2009
1) Let V be a vector space with basis . Let x,y V with coordinates relative to B of cfw_c1,c2,
, cn and cfw_d1, d2, dn respectively.
a. Find coordinates for x + y and kx relative to B.
and so
and
Simil
MAT 272 Assignment #5
Due: October 27, 2009
1) Show that the set V of all 23 matrices is a vector space.
2) Show that the set H of 23 matrices of the form is a subspace of the vector space V in
#1.
3) Show that the set of polynomials of the form is a vect
MAT 272 Assignment #5
Due: October 27, 2009
1) Show that the set V of all 23 matrices is a vector space.
Let
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
x)
2) Show that the set H of 23 matrices of the form
is a subspace of the vector
space V in #1.
i)
ii)
iii)
MAT 272 Assignment #5
Due: October 27, 2009
1) Show that the set V of all 23 matrices is a vector space.
Let
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
x)
2) Show that the set H of 23 matrices of the form is a subspace of the vector space V in
#1.
i)
ii)
iii)
MAT 272 Assignment #4
Due: October 15, 2009
1) Calculate the following determinants using cofactor expansion. Show your work.
a.
b.
2) Let A = and k = -2. Verify that det(kA) = k3det(A).
3) Let A = . Verify that det(A) = det(AT).
4) Given that . Calculate
MAT 272 Assignment #4
Due: October 15, 2009
1) Calculate the following determinants using cofactor expansion. Show your work.
a.
b.
2) Let A =
(-2)A =
and k = -2. Verify that det(kA) = k3det(A).
det(-2A) = -448
(-2)3det(A) = (-8)det(A) = -448.
3) Let A =
MAT 272 Assignment #4
Due: October 15, 2009
1) Calculate the following determinants using cofactor expansion. Show your work.
a.
b.
2) Let A = and k = -2. Verify that det(kA) = k3det(A).
(-2)A = det(-2A) = -448
(-2)3det(A) = (-8)det(A) = -448.
3) Let A =
MAT 272 Assignment #3
Due: October 6, 2009
1) Plot the four vertices of the unit square (0,0), (1,0), (0,1), (1,1) and also plot the images
of the four vertices using the following transformations T(x) = Ax on . Describe the
effect of each one.
a. A=
b. A
MAT 272 Assignment #3
Due: October 6, 2009
1) Plot the four vertices of the unit square (0,0), (1,0), (0,1), (1,1) and also plot the images
of the four vertices using the following transformations T(x) = Ax on . Describe the
effect of each one.
a. A=
Refl
MAT 272 Assignment #3
Due: October 6, 2009
1) Plot the four vertices of the unit square (0,0), (1,0), (0,1), (1,1) and also plot the images
of the four vertices using the following transformations T(x) = Ax on . Describe the
effect of each one.
a. A=
Refl
MAT 272 Assignment #2
Due: September 22, 2009
1) Solve the following linear systems. Write solutions in parametric form.
a.
b.
c.
d.
2) Let u and v both be solutions to the matrix equation Ax = 0. Show that any linear
combination of u and v is also a solu
MAT 272 Assignment #2 - Solutions
Due: September 22, 2009
1) Solve the following linear systems. Write solutions in parametric form.
a.
b.
c.
d.
2) Let u and v both be solutions to the matrix equation Ax = 0. Show that any linear
combination of u and v is
MAT 272 Assignment #2 - Solutions
Due: September 22, 2009
1) Solve the following linear systems. Write solutions in parametric form.
a.
b.
c.
d.
2) Let u and v both be solutions to the matrix equation Ax = 0. Show that any linear
combination of u and v is
MAT 272 Assignment #1
Due: September 15, 2009
1) Write the following system of equations as an augmented matrix.
2) Write the system of equations described by this augmented matrix.
3) Convert to reduced row echelon form using row operations.
4) Solve the
MAT 272 Assignment #1
Due: September 15, 2009
1) Write the following system of equations as an augmented matrix.
2) Write the system of equations described by this augmented matrix.
3) Convert to reduced row echelon form using row operations.
4) Solve the
MAT 272 Assignment #1
Due: September 15, 2009
1) Write the following system of equations as an augmented matrix.
2) Write the system of equations described by this augmented matrix.
3) Convert to reduced row echelon form using row operations.
4) Solve the
D. Burns
Math 272 - Exam I
11/8/11
Answer all questions completely. All questions have equal weight. Use your own paper or the
scratch paper provided. Show all necessary work.
1) Determine if the following system is consistent or inconsistent. Explain why
D. Burns
Math 272 - Exam I
11/8/11
Answer all questions completely. All questions have equal weight. Use your own paper or the
scratch paper provided. Show all necessary work.
1) Determine if the following system is consistent or inconsistent. Explain why