Chapter 6

Question 1

Calculate Matrix Magnitude

Answer 1

1. Multiply matrix by itself. (Should be 1x1)
2. Result is squared.

Question 2

Compute Unit Vector

Answer 2

1. Compute Magnitude
2. ( 1 / ||w|| ) * w

Question 3

Distance between two vectors

Answer 3

1. Subtract element wise.
2. Compute magnitude (result)

Question 4

Identify if set is orthogonal

Answer 4

1. Multiply elementwise between vectors
2. Add components. Must be equal to 0
   Keep in mind u1 + u2 = 0 , u2 + u3 = 0, etc.

Question 5

Express Y as Linear Combination

Answer 5

1. C = ( y * u ) / u * u
   for every basis vector
2. Combine into equation Y = C1U1 + C2U2 + C3U3

Question 6

Calculate yHat / Span / Orthogonal Projection

Answer 6

1. (( y * u ) / (u * u) ) * U

Question 7

Orthogonal Projection is also known as

Answer 7

Span

Question 8

Span is also known as

Answer 8

Orthogonal projection

Question 9

What is an orthonormal set

Answer 9

1. Orthogonal Set
2. Vectors are “unit vectors”

Question 10

What is a Unit Vector

Answer 10

Magnitude of 1.
u * u = 1