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CSET Linear Algebra

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. 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>> .






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






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






4. (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.






5. 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>






6. 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)






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






8. Sum of last two digit divisible by 4






9. Product of two numbers divided by greatest common denominator






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






11. 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






12. Vector that describes direction and speed






13. Divisible by 2 and 3






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






15. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically






16. Is commutative - associative






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






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






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






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






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






22. 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






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






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






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






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






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






28. On X - Y and Z plane






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






30. Equals the magnitude of the cross product






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






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






33. Must be scalar multiples of each other






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






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






36. 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)






37. Dot product must equal zero






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






39. Magnitude and direction






40. 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






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






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






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






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