In Exercises 16-18, determine whether the given ( 2 × 3 ) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equations of the form x = a t + b , y = c t + d , z = e t + f . x 1 + 3 x 2 − 2 x 3 = − 1 2 x 1 + 6 x 2 − 4 x 3 = − 2
In Exercises 16-18, determine whether the given ( 2 × 3 ) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equations of the form x = a t + b , y = c t + d , z = e t + f . x 1 + 3 x 2 − 2 x 3 = − 1 2 x 1 + 6 x 2 − 4 x 3 = − 2
Solution Summary: The author explains that the given (2times 3) system of linear equations represents coincident planes, two parallel, or two whose intersection is line, and gives parametric equation
In Exercises 16-18, determine whether the given
(
2
×
3
)
system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equations of the form
x
=
a
t
+
b
,
y
=
c
t
+
d
,
z
=
e
t
+
f
.
x
1
+
3
x
2
−
2
x
3
=
−
1
2
x
1
+
6
x
2
−
4
x
3
=
−
2
In Exercises 9 write a vector equation that is equivalent to the given system of equations.
In Exercises 5 write a system of equations that is equivalent to the given vector equation.
Use the parametric equations to describe the solution sets of the given linear systems.
6 x 1 + 2 x 2 3 x 1 + x 2 = − 8 = − 4
2 x − y + 2 z 6 x − 3 y + 6 z − 4 x + 2 y − 4 z = − 4 = − 12 = 8
2. Solve the given linear system by both Gaussian and Gauss-Jordan elimination.
− 2 b + 3 c 3 a + 6 b − 3 c 6 a + 6 b + 3 c = 1 = − 2 = 5
Chapter 1 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
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