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.) 42. (T/F-C) If v 1 , … , v 4 are in R 4 and v 3 is not a linear combination of v 1 , v 2 , v 4 , then v 1 , v 2 , v 3 , v 4 is linearly independent.
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.) 42. (T/F-C) If v 1 , … , v 4 are in R 4 and v 3 is not a linear combination of v 1 , v 2 , v 4 , then v 1 , v 2 , v 3 , v 4 is linearly independent.
Solution Summary: The author explains that a set of vectors in Rn is linearly dependent if there are weights.
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.)
42. (T/F-C) If
v
1
,
…
,
v
4
are in
R
4
and
v
3
is not a linear combination of
v
1
,
v
2
,
v
4
, then
v
1
,
v
2
,
v
3
,
v
4
is linearly independent.
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
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