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