Unit 5: Investigating Linear Algebra and Matrices

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Across
  1. 4. a function whose value you want to minimize (like cost) or maximize (like profit).
  2. 8. a matrix that, when multiplied by A results in the identity. In a 2x2; Swap the positions of a and d, put negatives in front of b and c, and divide everything by ad−bc .
  3. 10. A special number that can be calculated from a square matrix.
  4. 16. a matrix in which the entries outside the main diagonal are all zero
  5. 18. the number of rows by the number of columns. If a matrix has a rows and b columns, it is an a×b matrix
  6. 20. any prescribed way of assigning to each object in one set a particular object in another (or the same) set.
  7. 23. Two or more equations that share variables.
  8. 25. those variables whose values can vary over the feasible set of alternatives in order to either increase or decrease the value of the objective function.
  9. 26. An equation that is true no matter what values are chosen.
  10. 27. An arrangement of figures, one above the other.
  11. 28. A method to find the best solution when there are linear equations and/or inequalities.
  12. 30. how the numbers in an addition/multiplication problem are grouped doesn’t change the solution
  13. 31. "Flipping" a matrix over its diagonal. The rows and columns get swapped. The symbol is a "T" placed above and to the right like this: A^T
  14. 32. A limitation on the possible values of variables in a model, often expressed by an equation or inequality or by specifying that the value must be an integer.
  15. 35. pairs of mathematical manipulations in which one operation undoes the action of the other—for example, addition and subtraction, multiplication and division.
Down
  1. 1. a set that is closed under finite vector addition and scalar multiplication.
  2. 2. System that has no solution.
  3. 3. the multiplication of a vector by a scalar (where the product is a vector),
  4. 5. is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints,
  5. 6. a square matrix over a commutative ring is invertible if and only if its determinant is a unit in that ring.
  6. 7. one of the objects that are connected together.
  7. 9. a point in a convex set which does not lie in any open line segment joining two points in the set.
  8. 11. a matrix with rows and columns labeled by graph vertices, …
  9. 12. (1) In each row, the leftmost nonzero entry is 1 and the column that contains this 1 has all other entries equal to 0. This 1 is called a leading 1 (2)The leading 1 in the second row or beyond is to the right of the leading 1 in the row just above.(3) Any row containing only 0's is at the bottom.
  10. 13. quantities that only have magnitude (or size),
  11. 14. the order in which two numbers are added/multiplication does not change the solution
  12. 15. A flat surface with no thickness. It extends forever.
  13. 17. has at least one solution,
  14. 19. function A function whose graph is a straight line or describes a gradual rate of change, either positive or negative.
  15. 21. matrix used to represent a finite graph
  16. 22. the only matrix whose rank is 0.
  17. 24. a one-dimensional figure, which has length but no width and is made of a set of points which is extended in opposite directions infinitely with zero curvature
  18. 26. It is an involutory matrix, equal to its own inverse.
  19. 29. An array of numbers. They can be added, subtracted, multiplied and more.
  20. 33. Things lying side-by-side. Objects, people, numbers, etc in a horizontal line.
  21. 34. A quantity with magnitude and direction in the plane or in space, defined by an ordered pair or triple of real numbers.