Name: Linear ggebra I NYC (Sec3)
[2 each] 1. The following matrices are augmented matrices. Without solving the system,
determine how many solutions it has. Ifthere are inﬁnitely many solutions, determine
the number of parameters present,
0 1 1 o
1 1 2 3
L’HEOREM 1.7.4
EXERCISE SET
1.7
Then
1 3 10 —2 —11
l _
AM: —2 o [3 (2) :]= —2 4 —8
4 —5 —11 —8 41
1 3
Observe that ATA and AAT are symmetric as expected. >
general conditions on A under which AA7 and A'
are invertible. However, in the special case where A
Cryptography
Cryptography is the process of coding and decoding messages. The word comes
from the Greek kryptos, meaning “hidden.” The technique can be traced back to
the ancient Greeks. Today governments use sophisticated methods of coding and
. decoding
5 General Vector Spaces
The Zero Vector Space
Let V consist of a single object, which we denote by 0, and deﬁne
0+0=0 and k0=0
for all scalars k. It is easy to check that all the vector space axioms are satisﬁed. We call
this the zero vector space.
As we
a Chapter 5 / General Vector Spaces
£532? 5.2.4
.CISE SET
Spanning sets are not unique. For example, any two noncollinear vectors that lie in
the plane shown in Figure 5.2.5 will span that same plane, and any nonzero vector on
the line in that ﬁgure will
Solemn
Test 3 (Version 1)
Student ID number:
Student Name :
Initials:
instructions (Please read carefully)
General Instructions
- Time : 120 minutes
- Permitted materials: - 3" x 5" formula sheet. handwritten. one side only. plus the two 3” x 5"
formula
Ie_st g - Day
Student ID number: Student Name :
Instructions (Please read carefully)
General Instructions
- Time : 60 minutes
* Permitted materials: — 3" x 5" formula sheet, handwritten. one side only + 3" x 5" formula
sheet from previous test
- Pens. Pen
[20 Mtg
goy[uLCO'/j ‘05 310070
a“;
YBTestl Da i ns
Student to number:
Student Name :
initials:
Instructions (Please read carefully)
General Instructions
Time : 120 minutes
Permitted materials: - 3" x 5" formula sheet. handwritten. one side only
- Pens
Test 3 (Version 1)
Student ID number:
_
Student Name :
_
Initials:
_
Instructions (Please read carefully)
General Instructions
Time :
120 minutes
Permitted materials:
- 3' x 5' formula sheet, handwritten, one side only, plus the two 3' x 5'
formula sheets
Test 2 (Version 1)
Student ID number:
_
Student Name :
_
Initials:
_
Instructions (Please read carefully)
General Instructions
Time :
120 minutes
Permitted materials:
- 3' x 5' formula sheet, handwritten, one side only + 3' x 5' formula
sheet from previou
Test 1 (Version 1)
Student ID number:
_
Student Name :
_
Initials:
_
Instructions (Please read carefully)
General Instructions
Time :
120 minutes
Permitted materials:
- 3' x 5' formula sheet, handwritten, one side only
- Pens, Pencils, Rulers, Protractors
Sample Test
Student ID number:
_
Student Name :
_
Initials:
_
Instructions (Please read carefully)
General Instructions
Time :
120 minutes
Permitted materials:
- 3' x 5' formula sheet, handwritten, one side only
- Pens, Pencils, Rulers, Protractors, Erase
Right hand Rules
Physics NYB
Math and NYA
Force of a magnetic field on a moving charged particle
RH-Coordinate System
Force of a magnetic field on a current carrying wire
Direction of the torque caused by a force turning a wheel
Direction of the magnetic