©Zarestky
Math 141 Quiz 3 Version B
9/17/2009
NAME:______KEY__________________________________
1.
(3 pts) Solve the following system of equations by using Gauss-Jordan elimination by hand. For full
credit, indicate all row operations with the appropriate notation. (Hint: There is only one step left!)
" 1 !4 !9 %
$
'
# 0 1 5 &
2.
4R2 + R1 ! R1
! 1 0 11 $
#
&
" 0 1 5 %
(4 pts) The following matrix is in row-reduced form and represents a system with infinitely many
solutions. Write the parametric form of the solution.
" 1 3 !7 %
$
'
$ 0 0 0 '
$#
'&
x + 3y = !7
y=t
x = !3y !7 = !3t !7
The solution is (!3t !7,t ).
3.
Solution is (11, 5).
Alternative solution:
x=t
1
7
1
7
y =! x! =! t!
3
3
3
3
"
1
7%
The solution is $$$t,! t ! '''.
3
3 '&
#
(3 pts) What is entry a21 in the matrix that results from the calculation shown below?
!
A= #
"
!
=#
#"
T
r s $ ! '1 2 r $ = ! r 1 $ ! '1 2 r $
& #
& #
&#
&
1 0 % " 0 s 4r % " s 0 % " 0 s 4r %
r 2r + s r 2 + 4r $
&
's
2s
rs
&%
a21 = !s