Give an algebraic proof for thetriangleinequality ‖ v → ‖ ≤ ‖ w → ‖ + ‖ v → ‖ w → . . Drawasketch.Hint:Expand ‖ v → + w → ‖ 2 = ( v → + w → ) ⋅ ( v → + w → ) . Then use the Cauchy-Schwarz inequality.
Give an algebraic proof for thetriangleinequality ‖ v → ‖ ≤ ‖ w → ‖ + ‖ v → ‖ w → . . Drawasketch.Hint:Expand ‖ v → + w → ‖ 2 = ( v → + w → ) ⋅ ( v → + w → ) . Then use the Cauchy-Schwarz inequality.
Solution Summary: The author explains the triangle inequality Vert'stackrel' to a given value.
Give an algebraic proof for thetriangleinequality
‖
v
→
‖
≤
‖
w
→
‖
+
‖
v
→
‖
w
→
.
. Drawasketch.Hint:Expand
‖
v
→
+
w
→
‖
2
=
(
v
→
+
w
→
)
⋅
(
v
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. Then use the Cauchy-Schwarz inequality.
Let f : {0, 1}2 → {0,1}³.f(x) = x0.
1) What is the range of the function?
2) Is f one-to-one? Justify your answer.
3) Is f onto? Justify your answer.
4) Is f a bijection? Justify your answer.
Indicate on an xy-plane those points (x, y) for which the statement holds.
|x − 3| ≤ 5 and |y + 2| < 5
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