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