Test your basic knowledge |

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. Equals the magnitude of the cross product






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






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






4. Magnitude and direction






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






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






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






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






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






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






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. Dot product must equal zero






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






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






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






16. Is commutative - associative






17. 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)






18. (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.






19. 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>






20. (0 -0) in two dimensions - (0 -0 -0) in three. magnitude is 0 and no direction - it is a point geometrically






21. Vector that describes direction and speed






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






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






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






26. Must be scalar multiples of each other






27. 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>> .






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






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






31. 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






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






33. Sum of last two digit divisible by 4






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






36. On X - Y and Z plane






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






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






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






40. Product of two numbers divided by greatest common denominator






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






42. Divisible by 2 and 3






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






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