2) Introduction to Matrices Flashcards
When are two matrices equal
Two matrices are said to be equal if they are of the same size (i.e. they have the same real number of rows and columns) and their corresponding entries are equal
What is a column vector
What is the sum of matrices and the scalar of matrices
- (A + B)ij = Aij + Bij
- (λA)ij = λAij
What is a linear combination
How is the product of 2 matrices written
Let A be a mxn matrix and B be a nxp matrix
What is a diagonal matrix
An n × n matrix is called diagonal if all the entries which are not on the diagonal are 0
What is an identity matrix
The n×n identity matrix is the n×n diagonal matrix such that every diagonal entry is 1
What is a scalar matrix
An n × n matrix is a scalar matrix if it is a diagonal matrix all of whose diagonal entries are equal
What are the applications of matrices
- Differential equations
- Grayscale images
- Representing transformations of space
What are the elementary row operations
What is the inverse of a matrix
What is the a non-interviable matrix called
A singular matrix
Describe the proof that every invertible matrix has a unique inverse
Describe the proof that
What is the condition for a 2x2 matrix to be invertiable
Describe the proof of the conditon for an invertiable matrix (Do not need to knw)
What is the tranpose of a matrix
What are the properties of transposing a matrix
Describe some of the proof of the properties of transposing a matrix
Describe the proof that
