Solving Linear Systems Using Matrices

Question 1

a linear system is consistent if

Answer 1

it has at least one solution

Question 2

a linear system is inconsistent if

Answer 2

it has no solutions

Question 3

a matrix is in row echelon form when

Answer 3

• a row with only 0s is at bottom of the matrix

- if two successive rows are non 0, the second row starts with more 0s than the first

Question 4

a matrix is in reduced row echelon form when

Answer 4

• it is in row echelon form
• leading non 0 entry in each row is 1
• all other elements in the column with leading 1 must be 0s

Question 5

what are the elementary row operations we can use

Answer 5

• interchanging two rows
• multiplying rows by a non 0 scalar
• adding a multiple of one row to another row

Question 6

what are row equivalent matrices

Answer 6

when one matrix is obtained from another by using elementary row operations

Question 7

guass jordan elimination is used for

Answer 7

puttinga matrix into reduced row echelon form

Question 8

how could we tell a linear system is inconsistent

Answer 8

there is a row in which a non zero number is equal to 0,

Question 9

how can we tell a linear system has an infinite number of solutions

Answer 9

usually the number of unknowns is greater than the number of equations

Question 10

how to solve a linear system with infinitely many solutions

Answer 10

introduce parameters for unkowns