Questions:
Matrices and Linear Systems of Equations
The augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate operations and describe the solution set of the original system.
1) ( 173 - 4 )
( 01 - 13)
( 0001 )
( 001 - 2)
2) ( 1 - 100 - 4 )
( 01 - 30 - 7)
( 001- 3 - 1 )
( 00024 )
Solve the system.
3) x2 + 4x3 = -5
x1 + 3x2 + 5x3 = -2
3x1 + 7x2 +7x3 = 6
4) x1 + 3x3 = 8
2x1 + 2x2 + 9x3 = 7
x2 + 5x3 = -2
Determine if the system is consistent. Don not completely solve but explain your answer.
5) x1 + 3x3 = 2
x2 - 3x4 = 3
-2x2 + 3x3 +2x4 = 1
3x1 + 7x4 = -5
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.
6) ( 13 - 2)
( -4h8 )
Mark true or false and explain your answer.
a) every elementary row operation is reversible.
b) A 5x6 matrix has 6 rows.
c) The solution set of a linear system involving variables is a list of numbers ( ) that makes each equation in the system a true statement when the values are substituted for , respectively.
d) Two fundamental questions about a linear system involve existence and uniqueness.