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