sample_test4-answers - MATH 1711 Practice ProblemsSolutions Test 4 1 Denitions formulas and theorems(a What are the three legal row operations in

sample_test4-answers - MATH 1711 Practice ProblemsSolutions...

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MATH 1711 Practice Problems—Solutions Test 4 1. Definitions, formulas, and theorems(a) What are the three legal row operations in Gauss-Jordan elimination?(b) How many rows and columns does anm×nmatrix have?(c) What is avector?(d) What is the product of a row vector and a column vector?(e) When can you multiply anm×nmatrix times ak×matrix?(f) What is the product of anm×nmatrix and ann×kmatrix?(g) True or false?: If during Gauss-Jordan elimination you get a row of all 0s with a 0on the right-hand side, then there are infinitely many solutions.(h) True or false?: IfAandBare two matrices, thenA·Balways equalsB·A.(i) True or false?: IfAis a square matrix, thenA·Ais always defined.(j) IfA·Bis defined, how do you find its bottom-right entry?(k) What is then×nidentity matrix?(l) IfAis ann×nmatrix, define theinverse matrixofA.(m) True or false?: If you row-reduce the augmented matrix [A|I] and obtain a row ofzeros on the left-hand side, thenAis not invertible.(n) What is anobjective functionof a linear programming problem?(o) What is thefeasible setof a linear programming problem?(p) What is thefundamental theorem of linear programming? Solution: Page 1 of 7
MATH 1711 Practice Problems—Solutions Test 4

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