Understanding Vector Coordinates and Transition Matrices

The video tutorial explains how to find the B coordinates of a vector given its coordinates relative to the standard basis. It covers the concept of transition matrices, their inverses, and how to use them to convert coordinates. The tutorial includes a step-by-step process of finding the inverse of a matrix formed by basis vectors and using it to calculate the B coordinates of a vector. The final result shows the B coordinates of the vector as (-2, 2).

What are the given coordinates of vector X relative to the standard basis?

• 8, 12

• 12, 8

• 10, 18

• 18, 10

What is the relationship between the transition matrix from S to B and the transition matrix from B to S?

• They are unrelated

• They are equal

• The transition matrix from S to B is the inverse of the transition matrix from B to S

• The transition matrix from B to S is the inverse of the transition matrix from S to B

What is the first column of the matrix formed using the basis vectors from set B?

• -7, -4

• 2, 1

• -4, -7

• 1, 2

What is the second column of the matrix formed using the basis vectors from set B?

• 2, 1

• -7, -4

• -4, -7

• 1, 2

What is the first row of the inverse matrix?

• -2, 1

• 1, -2

• 4, -7

• -7, 4

What is the second row of the inverse matrix?

• -7, 4

• -2, 1

• 1, -2

• 4, -7

How is the first B coordinate of vector X calculated?

• -2 times 18 plus 1 times 10

• 7 times 18 plus -4 times 10

• 4 times 18 plus -7 times 10

• 1 times 18 plus -2 times 10

How is the second B coordinate of vector X calculated?

• 4 times 18 plus -7 times 10

• 1 times 18 plus -2 times 10

• -2 times 18 plus 1 times 10

• 7 times 18 plus -4 times 10

What are the final B coordinates of vector X?

• -2, 2

• 2, -2

• 18, 10

• 10, 18

What is the purpose of finding the B coordinates of vector X?

• To find the direction of vector X

• To convert from standard basis to B coordinates

• To find the magnitude of vector X

• To convert from B coordinates to standard basis