Linear algebra

Question 1

If a linear system has n variables and m equations,
then the augmented matrix has n rows.

Answer 1

false) rows depends on how many equations

Question 2

A consistent linear system must have infinitely
many solutions.

Answer 2

False) the system x+y =0, x-y=0 is consistent but x=0= y is the only solution

Question 3

If a row operation is done to a consistent linear system, the resulting system must be consistent

Answer 3

True) the result system will have at least one solution therefore will be consistent

Question 4

If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.

Answer 4

True) if og system is consistent the final system would be as well, same set solutions

Question 5

If there is more than one solution, A has a row of zeros

Answer 5

True)

Question 6

If A has a row of zeros, there is more than one
solution.

Answer 6

False) A=[1 0 |1]
[0 1 | 1]
[0 0 | 0]

Question 7

If there is no solution, the reduced row-echelon form of C has a row of zeros

Question 8

If the row-echelon form of C has a row of zeros, there is no solution

Answer 8

False) A= [ 1 0 | 1]
[ 0 1 | 1]
[ 0 0 | 0]

Question 9

There is no system that is inconsistent for every choice of constants.

Question 10

If the system is consistent for some choice of constants, it is consistent for every choice of constants

Answer 10

False) the system 2x - y = 0, -4x + 2y = 0 is consistent, but the system 2x - y =1, -4x + 2y=1 is not consistent