In Exercises 5 and 6, follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form. 6. x 1 + 3 x 2 − 5 x 3 = 0 x 1 + 4 x 2 − 8 x 3 = 0 − 3 x 1 − 7 x 2 + 9 x 3 = 0
In Exercises 5 and 6, follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form. 6. x 1 + 3 x 2 − 5 x 3 = 0 x 1 + 4 x 2 − 8 x 3 = 0 − 3 x 1 − 7 x 2 + 9 x 3 = 0
In Exercises 5 and 6, follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form.
6.
x
1
+
3
x
2
−
5
x
3
=
0
x
1
+
4
x
2
−
8
x
3
=
0
−
3
x
1
−
7
x
2
+
9
x
3
=
0
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form.
5. Write the solution set of the given homogeneous system in parametric vector form.
Verify that the given vector is the general solution of the corresponding homogeneous system, and then solve the nonhomogeneous system. Assume that t>0.
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