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CSET Linear Algebra

Subjects : cset, math, algebra
  • Answer 44 questions in 15 minutes.
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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. Sum of last two digit divisible by 4

2. Vector that describes direction and speed

3. Matrix 3x3: i j k a1 a2 a3 b1 b2 b3 i (a2a3/b2b3) - j(a1a3/b1b3) + k (a1a2/b1b2)= <i - j - k>

4. Square matrix with ones diagonally and zeros for the rest.

5. 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

6. Multiply first row by first column - add. Multiply first row by second column - add. Mxn multiply by next. Not necessarily commutative

7. A matrix that can be multiplied by the original to get the identity matrix

8. |a?xb?|=|a?||b?|sin? | = | a?. ? is the angle between a? and b? and is restricted to be between 0

9. |A|=Ax2+Ay2 ?=tan -1(Ay/Ax)

10. Sum of numbers divisible by three - number is divisible by 3.

11. If a? and b? are vectors and ? is the angle between them - the dot product denoted by a?

12. Show statement is true for n=1 - then show it is ture for K+1

13. To find the minor of an element in a matrix - take the determinant of the part of the matrix without that element.

14. Is commutative - associative

15. 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)

16. Numbers that are a sum of all of their factors. 6 - 8 - 128

17. Magnitude and direction

18. If a? and b? are two vectors - <a1 - a2> and <b1 - b2> - the dot product of a?and b? is defined as a?

19. Dot product must equal zero

20. F ? is the angle between vector A? and the x- axis - then Ax=Acos??Ay=Asin?? EX. If ?= 60

21. Product of two numbers divided by greatest common denominator

22. A vector with a magnitude of 1. the positive X- axis is vector i - pos. <1 -0> y xis is vector j <0 -1>

23. 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>> .

24. Or norm - of a vector using the distance formula. |v|=(x2-x1)2+(y2- y1)2. (square each component of vector)

25. Vector a +vector b is placing head of a next to tail of b and sum is a new vector

26. Same as triangle law except resultant vector is a diagonal of a parallelogram

27. 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>

28. Equals the magnitude of the cross product

29. (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.

30. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically

31. Every integer greater than 1 can be expressed as product of prime numbers

32. Switch the direction of one vector and add them (tail to head)

33. Vectors with same magnitude but are in opposite directions (+?-)

34. Follows same rules as scalar - but done component by component - and produces another vector (resultant)

35. Divisible by 2 and 3

36. (mk) + (mk -1)= (m+1k)

37. 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

38. Check for up to the square root of the number

39. Have same magnitude and direction - but possibly different starting points

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)

41. Must be scalar multiples of each other

42. On X - Y and Z plane

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

44. If the GCF is one - the numbers are relatively prime