Holooly Plus Logo
Holooly Plus Logo

Question 4.1.2: Adding Two Vectors in the Plane Find the sum of the vectors...

Adding Two Vectors in the Plane

Find the sum of the vectors.

a. u = (1, 4) , v = (2 , -2)

b. u = (3 , -2) , v= (-3 , 2)

c. u = (2 , 1) , v= (0 , 0)

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

a.  u + v = ( 1, 4) + (2 , -2) = (3 , 2)

b.  u + v = (3 , -2) + (-3 , 2) = (0 , 0) = 0

c.  u + v = (2 , 1) + ( 0 , 0 ) = (2 , 1)

Figure 4.4 gives a graphical representation of each sum.

Screenshot 2022-11-28 175933

Related Answered Questions

Question: 4.8.7

Rotation of a Conic Section Perform a rotation of axes to eliminate the xy-term in 5x² – 6xy + 5y² + 14√2x – 2√2y + 18 = 0 and sketch the graph of the resulting equation in the x´y´-plane. ...

Verified Answer:

The angle of rotation is given by cot 2θ = ...
Question: 4.8.6

A Transition Matrix for Rotation in R² Find the coordinates of a point (x, y) in R² relative to the basis B′ = {(cos θ, sin θ), (-sin θ, cos θ)}. ...

Verified Answer:

By Theorem 4.21 you have [B´   B] = \left [...
Question: 4.7.5

Finding a Transition Matrix Find the transition matrix from B to B´ for the following bases for R². B = {(-3, 2), (4, -2)} and B´ = {(-1, 2), (2, -2)} ...

Verified Answer:

Begin by forming the matrix [B´   B] = \lef...
Question: 4.7.4

Finding a Transition Matrix Find the transition matrix from B to B´ for the following bases for R³. B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and B = {(1, 0, 1), (0, -1, 2), (2, 3, -5)} ...

Verified Answer:

First use the vectors in the two bases to form the...
Question: 4.7.3

Finding a Coordinate Matrix Relative to a Nonstandard Basis Find the coordinate matrix of x = (1, 2, -1) in R³ relative to the (nonstandard) basis B´ = {u1, u2, u3} = {(1, 0, 1), (0, -1, 2), (2, 3, -5)}. ...

Verified Answer:

Begin by writing x as a linear combination of [lat...
Question: 4.7.2

Finding a Coordinate Matrix Relative to a Standard Basis The coordinate matrix of x in R² relative to the (nonstandard) ordered basis B = {v1, v2} = {(1, 0), (1, 2)} is [x]B =[3 2]. Find the coordinate matrix of x relative to the standard basis B’ = {u1, u2} = {(1, 0), (0, 1)}. ...

Verified Answer:

Because [x]_B =\left [ \begin{matrix} 3 \\ ...
Question: 4.7.1

Coordinates and Components in R^n Find the coordinate matrix of x = (-2, 1, 3) in R³ relative to the standard basis S = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}. ...

Verified Answer:

Because x can be written as x = (-2, 1, 3) = -2(1,...
Question: 4.8.4

Testing a Set of Solutions for Linear Independence Determine whether {e^x, xe^x, (x + 1)e^x} is a set of linearly independent solutions of the linear homogeneous differential equation y″′ – 3y″ + 3y′ – y = 0. ...

Verified Answer:

As in Example 3, begin by verifying that each of t...
Question: 4.8.3

Testing a Set of Solutions for Linear Independence Determine whether {1, cos x, sin x} is a set of linearly independent solutions of the linear homogeneous differential equation y′′′ + y′ = 0. ...

Verified Answer:

Begin by observing that each of the functions is a...
Question: 4.8.1

A Second-Order Linear Differential Equation Show that both y1 = e^x and y2 = e^-x are solutions of the second-order linear differential equation y″ – y = 0. ...

Verified Answer:

For the function y_1 = e^x, you hav...