Linear Algebra

Question 1

Building Blocks of Linear Algebra

Answer 1

Vectors

Question 2

What are Vectors

Answer 2

quantities having both direction and magnitude compared to scalar quantities which have only magnitude.

Question 3

Scalar Quantities

Question 4

What do Vectors consist of?

Answer 4

In order to have direction and magnitude:
Must have two or more elements of data.

Question 5

Dimensionality of a vector

Answer 5

determined by the number of numerical elements in that vector.

Question 6

Cartesian coordinate system

Question 7

Velocities

Question 8

Formula for magnitude or length of a vector

Answer 8

square root of the sum of each vector component squared
vector 1 (squared) + vector 2 (squared) + vector 3 (squared)

Question 9

Scalar Multiplication

Question 10

Vector Addition

Question 11

Vector Subtraction

Question 12

Vector Dot Products

Question 13

Magnitude of a vector

Question 14

Angle Between two vectors

Question 15

Matricies

Question 16

Matrix Operations

Question 17

Matrix Multiplication

Question 18

Matrix Addition

Question 19

Special Matricies

Question 20

Identity Matrix

Question 21

Transpose Matrix

Question 22

Permutation Matrix

Question 23

Linear Systems in a Matrix Form

Question 24

Gauss-Jordan Elimination

Question 25

Row Echelon Form

Question 26

Inverse Matrices

Question 27

Inverse Matrix use cases:

Question 28

Singular Matrices

Question 29

NumPY Array

Answer 29

are n-dimensional array data structures that can be used to represent both vectors (1-dimensional array) and matrices (2-dimensional arrays).

Question 30

Initialize NumPY array

Question 31

NumPY array representation of a vector

Question 32

NumPY array representation of a matrix