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