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