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






2. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically






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






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






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






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






7. Divisible by 2 and 3






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






9. Product of two numbers divided by greatest common denominator






10. 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>






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






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






14. 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)






15. Is commutative - associative






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






17. 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






18. On X - Y and Z plane






19. 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>> .






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






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






22. Magnitude and direction






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






24. Dot product must equal zero






25. (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.






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






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






28. Sum of last two digit divisible by 4






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






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






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






32. Equals the magnitude of the cross product






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






34. Must be scalar multiples of each other






35. Vector that describes direction and speed






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






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






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






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






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






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






43. 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)






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