Each statement in Exercises 39—44 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21—28.) 39. (T/F-C) If v 1 , ... , v 4 are in R 4 and v 3 = 2 v 1 + v 2 , then v 1 , v 2 , v 3 , v 4 is linearly dependent.
Each statement in Exercises 39—44 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21—28.) 39. (T/F-C) If v 1 , ... , v 4 are in R 4 and v 3 = 2 v 1 + v 2 , then v 1 , v 2 , v 3 , v 4 is linearly dependent.
Solution Summary: The author explains that if the given statement is true or false, a set of two or more vectors is linearly dependent.
Each statement in Exercises 39—44 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21—28.)
39. (T/F-C) If
v
1
,
...
,
v
4
are in
R
4
and
v
3
=
2
v
1
+
v
2
, then
v
1
,
v
2
,
v
3
,
v
4
is linearly dependent.
Part a, b, c, d, and e
Please show all work so I understand!
Thank you!!
For Exercises 66–68, find the indicated value.
a. v. w
b. v. v
66. v = (12, 8), w = (-3, –5)
1
8
3
67. v =
-i+
2
3j, w = -8i -
%3D
68. v = - 14i + j, w = 80i
30j
Elementary Algebra: Concepts and Applications (10th Edition)
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