MAT342 - Answers - Quiz 4 - Fall 2015
1. (5 pts) Let A be a nonsingular matrix such that A1 = AT Prove that the determinant of A
is either 1 or 1
Proof:
|AT | = |A|, |A1 = 1/|A|,
this leads to the equ
MAT342: Exam 1
September 23, 2013
Write your name on each sheet. Show all work. When you are done, arrange the
answer sheets in order.
Exercise 1. Consider the system:
25 pts
2x1 + x2 4x3 6x4 = 5
x1 +
Linear Algebra MAT342:
Solution HW 6
October 25, 2013
1
Section 3.4
Ex. 8) 2pts
a) The vectors x1 , x2 cannot span R3 , since Span(x1 , x2 ) is a vector space of dimension
at most 2 and R3 has dimensi
MAT342 - Quiz 4 - Fall 2014
1. (5 pts) Let I denote the n n identity matrix and let A be the 2n 2n matrix
(
I I
0 I
(
Find its inverse.
Answer. Assume that
(
A1
I 0
0 I
has the block form
)
(
=
P Q
R
NAME
MAT 342, Quiz 6, Fall 2014
No calculators
1. (5 pts) Let V be a vector space and let S be a subspace of V . Give the precise definition
of a spanning set for the subspace S.
2. (5 pts) Define pre
NAME
MAT342 - Quiz 4 - Fall 2014
1. (5 pts) Let I denote the n n identity matrix and let A be the 2n 2n matrix
(
I I
0 I
)
Find its inverse.
2. (5 pts) Let A be a nonsingular matrix. Show that
(
)
det
NAME
MAT 342, Quiz 6, Fall 2014
No calculators
1. (5 pts) Let V be a vector space and let S be a subspace of V . Give the precise definition
of a spanning set for the subspace S.
Answer: A set cfw_x1
NAME
MAT342 - Quiz 4 - Spring 2015
1. (5 pts) Let A be a nonsingular matrix. Prove that
(
)
det A1 =
1
det(A)
2. (5 pts) Use Cramers rule to find the solution (x, y)T to the system of equations
e cos(
NAME
MAT 342, Quiz 5, Spring 2015
No calculators
1. (5 pts) Give the precise definition of
Span(v1 , v2 , , vk )
2. (5 pts) Let U and V be subspaces of a vector space W .
(a) Define U + V .
(b) Prove
NAME
MAT 342, Quiz 5, Fall 2014
No calculators
1. (5 pts) Give the precise definition of a subspace.
Let V be a vector space. A nonempty subset of V is said to be a subspace if it is closed
under addi
NAME
MAT 342, Quiz 6, Fall 2014
No calculators
1. (5 pts) Let V be a vector space and let S be a subspace of V . Give the precise definition
of a spanning set for the subspace S.
Answer. The set cfw_v
NAME
MAT 342, Quiz 5, Fall 2014
No calculators
1. (5 pts) Give the precise definition of a subspace.
2. (5 pts) Use Cramers rule to solve the system for x and y: ax + by = 1, bx + ay = 1.
CIRCLE YOUR
NAME
MAT 342, Quiz 6, Spring 2015
No calculators
1. (3 pts) Complete the following definition: The vectors v1 , v2 , . . . , vn in the vector
space V are said to be linearly independent if
2. (3 pts)
Stretch Program Handout
ASUs Stretch
Program_
This handout is designed to help explain student placement in the Stretch
Program. It is also designed to help explain Stretch so that students
understand