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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. Product of two numbers divided by greatest common denominator






2. 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






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






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






5. Sum of last two digit divisible by 4






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






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






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






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






10. 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)






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






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






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






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






15. 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>






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






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






18. 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)






19. Magnitude and direction






20. Is commutative - associative






21. 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






22. Dot product must equal zero






23. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically






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






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






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






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






28. Equals the magnitude of the cross product






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






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






31. Must be scalar multiples of each other






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






33. (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.






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






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






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






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






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






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






40. Vector that describes direction and speed






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






42. 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>> .






43. Divisible by 2 and 3






44. On X - Y and Z plane