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Test your basic knowledge |
CSET Linear Algebra
Start Test
Study First
Subjects
:
cset
,
math
,
algebra
Instructions:
Answer 44 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Addition: A?+B?=<x1+x2 - y1+y2>or C?+D?=<x1+x2 - y1+y2 -z1+z2> Subtraction: A?- B?=<x1-x2 - y1- y2>or C?+D?=<x1-x2 - y1- y2 -z1-z2> Scalar Multiplication: kC?=k<x1 - y1 -z1>=<kx1 - ky1 - kz1>or kA?=k<x1 - y1>=<kx1 - ky1>
algebraic vector operations
dot product
Triangle (head to tail) law
unit vector
2. On X - Y and Z plane
orthogonal vectors
3- dimensional vectors
Inverse matrices
algebraic vector operations
3. If a? and b? are two vectors - <a1 - a2> and <b1 - b2> - the dot product of a?and b? is defined as a?
dot product definition
Scalar multiple
Cross product
unit vector
4. Divide bigger by smaller - dividing smaller by remainder - first remainder by second - second by third - until you have a remainder of 0. Last remainder is GCD (aka euclidean algorithm)
Identity matrix
Least common multiple
unit vector
Finding GCD
5. Divisible by 2 and 3
Least common multiple
Perfect numbers
divisibility rule for 6
divisibility rule for 4
6. Numbers that are a sum of all of their factors. 6 - 8 - 128
Multiplying matrices
Perfect numbers
dot product definition
parallel vectors
7. Sum of last two digit divisible by 4
How many primes to check for?
divisibility rule for 4
Vector addition
angle of vectors using cross product:
8. Vector that describes direction and speed
Perfect numbers
unit vector
Velocity vector
divisibility rule for 3
9. Every integer greater than 1 can be expressed as product of prime numbers
Fundamental theorem of arithmetic
Finding GCD
Opposite vectors
Velocity vector
10. Can multiple a vector by a scalar. components of vectors are the same - magnitude is IkI times the vector - direction depends on if k is pos. or neg
algebraic vector operations
How many primes to check for?
Scalar multiple
Multiplying matrices
11. A matrix that can be multiplied by the original to get the identity matrix
divisibility rule for 6
To prove by mathematical induction
dot product
Inverse matrices
12. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically
Identity matrix
If you know the x and Y component of a vector
parallel vectors
zero vector
13. Check for up to the square root of the number
How many primes to check for?
orthogonal vectors
Least common multiple
divisibility rule for 3
14. Two vectors are parallel if their components are multiples of each other. Ex. <2 -5> and <4 -10> are because 2(2 -5)= 4 -10
Vector has two things
Opposite vectors
divisibility rule for 4
Parallel vectors
15. To find the minor of an element in a matrix - take the determinant of the part of the matrix without that element.
Finding GCD
3- dimensional vectors
parallelogram law
Minors
16. F ? is the angle between vector A? and the x- axis - then Ax=Acos??Ay=Asin?? EX. If ?= 60
dot product
angle of vector
Perfect numbers
divisibility rule for 6
17. If a? and b? are vectors and ? is the angle between them - the dot product denoted by a?
unit vector
Finding GCD
Cross product
Angle of dot product
18. If the initial point of a vector has coordinate (x1 - y1)and the terminal point has coordinate (x2 - y2) - then the ordered pair that represents the vector is <x2-x1 - y2- y1>> .
algebraic vector operations
Algebraic vector ordered pair
Multiplying matrices
Perfect numbers
19. Same as triangle law except resultant vector is a diagonal of a parallelogram
zero vector
divisibility rule for 3
unit vector
parallelogram law
20. Is commutative - associative
dot product definition
To prove by mathematical induction
parallel vectors
Addition
21. Multiply first row by first column - add. Multiply first row by second column - add. Mxn multiply by next. Not necessarily commutative
Multiplying matrices
algebraic vector operations
Opposite vectors
Magnitude of a vector
22. Matrix 3x3: i j k a1 a2 a3 b1 b2 b3 i (a2a3/b2b3) - j(a1a3/b1b3) + k (a1a2/b1b2)= <i - j - k>
angle of vector
vector subtraction
Cross product
Angle of dot product
23. Switch the direction of one vector and add them (tail to head)
Opposite vectors
Identity matrix
orthogonal vectors
vector subtraction
24. |a?xb?|=|a?||b?|sin? | = | a?. ? is the angle between a? and b? and is restricted to be between 0
Relatively prime
Opposite vectors
Inverse matrices
angle of vectors using cross product:
25. Take the magnitude of the cross product of any two adjacent vectors of the form <a - b - c>(a - and b are y - y - x-x - and c can be zero)
orthogonal vectors
divisibility rule for 4
area of a parallelogram
parallel vectors
26. Magnitude and direction
Vector has two things
Triangle (head to tail) law
Magnitude of a vector
Velocity vector
27. Dot product must equal zero
orthogonal vectors
Addition
parallelogram law
Least common multiple
28. Does not matter what order you add them in - it will result in straight vector. If (n -1) numbers of vectors are represented by n -1 sides of a polygon - then the nth side is the sum of the vectors
angle of vector
dot product definition
To prove by mathematical induction
polygon law of vector addition
29. If the GCF is one - the numbers are relatively prime
zero vector
Relatively prime
parallel vectors
Perfect numbers
30. Square matrix with ones diagonally and zeros for the rest.
Cross product
Vector addition
Identity matrix
parallelogram law
31. Product of two numbers divided by greatest common denominator
Least common multiple
Opposite vectors
If you know the x and Y component of a vector
parallelogram law
32. A vector with a magnitude of 1. the positive X- axis is vector i - pos. <1 -0> y xis is vector j <0 -1>
area of a parallelogram
unit vector
divisibility rule for 4
orthogonal vectors
33. Have same magnitude and direction - but possibly different starting points
Equivalent vectors
3- dimensional vectors
unit vector
How many primes to check for?
34. (mk) + (mk -1)= (m+1k)
vector subtraction
Algebraic vector ordered pair
Pascals rule
zero vector
35. Vectors with same magnitude but are in opposite directions (+?-)
To prove by mathematical induction
Opposite vectors
area of a parallelogram
Velocity vector
36. (inner product)(scalar product) Result is scalar - large if vectors parallel - 0 if vectors perpendicular. Tells us how close vectors are pointing to same point.
orthogonal vectors
How many primes to check for?
dot product
unit vector
37. Or norm - of a vector using the distance formula. |v|=(x2-x1)2+(y2- y1)2. (square each component of vector)
unit vector
parallel vectors
Magnitude of a vector
Fundamental theorem of arithmetic
38. |A|=Ax2+Ay2 ?=tan -1(Ay/Ax)
How many primes to check for?
dot product
divisibility rule for 3
If you know the x and Y component of a vector
39. Sum of numbers divisible by three - number is divisible by 3.
Scalar multiple
Relatively prime
angle of vectors using cross product:
divisibility rule for 3
40. Vector a +vector b is placing head of a next to tail of b and sum is a new vector
parallel vectors
Triangle (head to tail) law
area of a parallelogram
Vector addition
41. Equals the magnitude of the cross product
Least common multiple
divisibility rule for 4
Area of a parallelogram
angle of vector
42. Show statement is true for n=1 - then show it is ture for K+1
vector subtraction
Addition
Triangle (head to tail) law
To prove by mathematical induction
43. Follows same rules as scalar - but done component by component - and produces another vector (resultant)
Area of a parallelogram
divisibility rule for 3
Vector addition
divisibility rule for 6
44. Must be scalar multiples of each other
parallel vectors
How many primes to check for?
Opposite vectors
Magnitude of a vector