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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. Product of two numbers divided by greatest common denominator
Least common multiple
Magnitude of a vector
Inverse matrices
area of a parallelogram
2. 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
polygon law of vector addition
divisibility rule for 4
Minors
Relatively prime
3. Follows same rules as scalar - but done component by component - and produces another vector (resultant)
area of a parallelogram
Vector addition
Minors
divisibility rule for 4
4. A vector with a magnitude of 1. the positive X- axis is vector i - pos. <1 -0> y xis is vector j <0 -1>
Vector has two things
How many primes to check for?
angle of vectors using cross product:
unit vector
5. Sum of last two digit divisible by 4
divisibility rule for 4
Fundamental theorem of arithmetic
Opposite vectors
area of a parallelogram
6. Have same magnitude and direction - but possibly different starting points
parallel vectors
Pascals rule
Scalar multiple
Equivalent vectors
7. 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
Scalar multiple
vector subtraction
Addition
Equivalent vectors
8. Sum of numbers divisible by three - number is divisible by 3.
divisibility rule for 3
angle of vector
Perfect numbers
divisibility rule for 4
9. Matrix 3x3: i j k a1 a2 a3 b1 b2 b3 i (a2a3/b2b3) - j(a1a3/b1b3) + k (a1a2/b1b2)= <i - j - k>
Minors
Opposite vectors
Cross product
Magnitude of a vector
10. 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)
Finding GCD
Relatively prime
parallel vectors
parallelogram law
11. Show statement is true for n=1 - then show it is ture for K+1
Parallel vectors
Least common multiple
To prove by mathematical induction
polygon law of vector addition
12. If a? and b? are vectors and ? is the angle between them - the dot product denoted by a?
Finding GCD
Angle of dot product
Least common multiple
Magnitude of a vector
13. Square matrix with ones diagonally and zeros for the rest.
Opposite vectors
Finding GCD
divisibility rule for 6
Identity matrix
14. |a?xb?|=|a?||b?|sin? | = | a?. ? is the angle between a? and b? and is restricted to be between 0
How many primes to check for?
angle of vectors using cross product:
Finding GCD
Vector addition
15. 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>
dot product definition
algebraic vector operations
Angle of dot product
orthogonal vectors
16. Multiply first row by first column - add. Multiply first row by second column - add. Mxn multiply by next. Not necessarily commutative
Multiplying matrices
Magnitude of a vector
Relatively prime
parallelogram law
17. Vectors with same magnitude but are in opposite directions (+?-)
To prove by mathematical induction
Opposite vectors
polygon law of vector addition
divisibility rule for 3
18. 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)
Fundamental theorem of arithmetic
parallelogram law
algebraic vector operations
area of a parallelogram
19. Magnitude and direction
Vector has two things
Inverse matrices
Parallel vectors
polygon law of vector addition
20. Is commutative - associative
angle of vectors using cross product:
polygon law of vector addition
Addition
dot product
21. 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 addition
Parallel vectors
Addition
Minors
22. Dot product must equal zero
area of a parallelogram
algebraic vector operations
orthogonal vectors
vector subtraction
23. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically
Pascals rule
Velocity vector
Least common multiple
zero vector
24. Same as triangle law except resultant vector is a diagonal of a parallelogram
Parallel vectors
Relatively prime
parallelogram law
Triangle (head to tail) law
25. |A|=Ax2+Ay2 ?=tan -1(Ay/Ax)
Vector addition
3- dimensional vectors
zero vector
If you know the x and Y component of a vector
26. Vector a +vector b is placing head of a next to tail of b and sum is a new vector
area of a parallelogram
Parallel vectors
parallelogram law
Triangle (head to tail) law
27. (mk) + (mk -1)= (m+1k)
Pascals rule
Fundamental theorem of arithmetic
divisibility rule for 4
dot product definition
28. Equals the magnitude of the cross product
Magnitude of a vector
If you know the x and Y component of a vector
Area of a parallelogram
3- dimensional vectors
29. Every integer greater than 1 can be expressed as product of prime numbers
parallelogram law
Fundamental theorem of arithmetic
Least common multiple
Inverse matrices
30. Or norm - of a vector using the distance formula. |v|=(x2-x1)2+(y2- y1)2. (square each component of vector)
3- dimensional vectors
Magnitude of a vector
Finding GCD
Triangle (head to tail) law
31. Must be scalar multiples of each other
polygon law of vector addition
Inverse matrices
parallel vectors
Angle of dot product
32. Check for up to the square root of the number
How many primes to check for?
Scalar multiple
algebraic vector operations
Velocity vector
33. (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.
Multiplying matrices
dot product
parallelogram law
divisibility rule for 3
34. To find the minor of an element in a matrix - take the determinant of the part of the matrix without that element.
angle of vectors using cross product:
If you know the x and Y component of a vector
Minors
Vector addition
35. Numbers that are a sum of all of their factors. 6 - 8 - 128
angle of vectors using cross product:
Identity matrix
Vector has two things
Perfect numbers
36. A matrix that can be multiplied by the original to get the identity matrix
algebraic vector operations
parallelogram law
Inverse matrices
dot product
37. If the GCF is one - the numbers are relatively prime
divisibility rule for 4
divisibility rule for 3
dot product definition
Relatively prime
38. Switch the direction of one vector and add them (tail to head)
vector subtraction
angle of vector
Scalar multiple
Identity matrix
39. If a? and b? are two vectors - <a1 - a2> and <b1 - b2> - the dot product of a?and b? is defined as a?
Minors
Velocity vector
dot product definition
angle of vectors using cross product:
40. Vector that describes direction and speed
area of a parallelogram
vector subtraction
Velocity vector
Opposite vectors
41. F ? is the angle between vector A? and the x- axis - then Ax=Acos??Ay=Asin?? EX. If ?= 60
angle of vector
area of a parallelogram
Least common multiple
divisibility rule for 6
42. 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>> .
Area of a parallelogram
vector subtraction
Inverse matrices
Algebraic vector ordered pair
43. Divisible by 2 and 3
orthogonal vectors
vector subtraction
Minors
divisibility rule for 6
44. On X - Y and Z plane
parallelogram law
Fundamental theorem of arithmetic
3- dimensional vectors
Angle of dot product