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






3. Vector that describes direction and speed






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






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






6. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically






7. Equals the magnitude of the cross product






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






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






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






11. 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






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>






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






14. 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>> .






15. Divisible by 2 and 3






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






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






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






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






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






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






23. Magnitude and direction






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






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






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






27. Is commutative - associative






28. 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)






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






30. 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>






31. Dot product must equal zero






32. Must be scalar multiples of each other






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






34. On X - Y and Z plane






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






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






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






38. 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






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






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






41. (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.






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






43. Sum of last two digit divisible by 4






44. 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