Understanding Vectors as Linear Combinations

The video tutorial explains how to express vectors as linear combinations of unit vectors i and j. It provides two examples: vector x1 with components 3 in the positive x direction and -2 in the negative y direction, and vector x2 with components -5 in the negative x direction and 2 in the positive y direction. The tutorial also demonstrates how to represent these vectors in component form using angle brackets and column matrices.

What is a unit vector in the positive x direction commonly referred to as?

• Vector x

• Vector i

• Vector k

• Vector j

In the first example, how many units is the x component of the vector?

• 3 units

• 2 units

• 5 units

• 4 units

How is the y component of the first example vector expressed?

• 2 times vector j

• -2 times vector j

• -3 times vector j

• 3 times vector j

What is the component form of the first example vector?

• (3, -2)

• (-3, 2)

• (-3, -2)

• (3, 2)

Which of the following represents the matrix form of the first example vector?

• [-3, -2]

• [-3, 2]

• [3, -2]

• [3, 2]

In the second example, what is the x component of the vector?

• -5 units in the positive x direction

• 5 units in the negative x direction

• -5 units in the negative x direction

• 5 units in the positive x direction

How is the y component of the second example vector expressed?

• 5 times vector j

• -2 times vector j

• -5 times vector j

• 2 times vector j

What is the component form of the second example vector?

• (5, -2)

• (-5, 2)

• (-5, -2)

• (5, 2)

Which of the following represents the matrix form of the second example vector?

• [5, 2]

• [-5, 2]

• [-5, -2]

• [5, -2]