Linear algebra: please solve q21 and 34 correctly and handwritten 20. Repeat Exercise 19 for u =BEand A (0.-1).21. Let u AB and v= CD, where A = (-1,2),B=(3,5), C = (0, 3), D = (4, -1).a) Find a point Q such that v = BQ andu + v = AQ.-24-b) Graph u = AB, v = CD, v = BQ, andu + v = AQ.22. Repeat Exercise 21 with A = (-2,4),B = (1, -3), C = (0, 1), D = (3,5).23. Let u == [₁3the point (-2, 1).a) Find points B and C such that u = AB,v = AC, and u- v = CB.-[-and v =and v =-2and let A denote27. Let v AB where A = (1, 4) and B = (5.-1).a) If C= (-2, 7), find D such that 2v = CD.b) Graph v= AB and 2v = CD.In Exercises 28-31, find a unit vector u that has the samedirection as the given vector v.[1]228. v =30. v = i + j-[³]431. v = 3i - 2j29. V =In Exercises 32-35, determine the terminal point B suchthat v= AB.32. v has the same direction as4√5, A=(-4,-2).33. v has opposite direction to3√10, A=(4,7).[²].||v|| =||v||=34. v is parallel to i +2j, A=(3, 1), B is on they-axis.35 y is parallel to i3i(31) R is on the line

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Answered: 21. Let u AB and v= CD, where A =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear algebra: please solve q21 and 34 correctly and handwritten

20. Repeat Exercise 19 for u =
BE
and A (0.-1).
21. Let u AB and v= CD, where A = (-1,2),
B=(3,5), C = (0, 3), D = (4, -1).
a) Find a point Q such that v = BQ and
u + v = AQ.
-2
4
-
b) Graph u = AB, v = CD, v = BQ, and
u + v = AQ.
22. Repeat Exercise 21 with A = (-2,4),
B = (1, -3), C = (0, 1), D = (3,5).
23. Let u =
= [₁
3
the point (-2, 1).
a) Find points B and C such that u = AB,
v = AC, and u- v = CB.
-[-
and v =
and v =
-2
and let A denote
27. Let v AB where A = (1, 4) and B = (5.-1).
a) If C= (-2, 7), find D such that 2v = CD.
b) Graph v= AB and 2v = CD.
In Exercises 28-31, find a unit vector u that has the same
direction as the given vector v.
[1]
2
28. v =
30. v = i + j
-[³]
4
31. v = 3i - 2j
29. V =
In Exercises 32-35, determine the terminal point B such
that v= AB.
32. v has the same direction as
4√5, A=(-4,-2).
33. v has opposite direction to
3√10, A=(4,7).
[²].
||v|| =
||v||
=
34. v is parallel to i +2j, A=(3, 1), B is on the
y-axis.
35 y is parallel to i3i
(31) R is on the line

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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