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