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