matrices Flashcards
What is a square matrix?
A matrix where there is the same number of rows and columns
What is a zero matrix? (2)
A matrix where every element is zero
The matrix is denoted by 0
What is an identity matrix?
A square matrix in which the numbers in the leading diagonal (top left to bottom right) are 1 and the other elements are zero
How are identity matrices denoted?
Ik where k (sub-script) is equal to the dimensions of the matrix
How are matrices added and subtracted?
Add or subtract the corresponding elements in the two matrices
What does additively conformable mean?
Two matrices that are the same size (meaning they can be added or subtracted)
How do you multiply a matrix by a scalar?
Multiply all of the elements by the scalar
How are matrices multiplied together?
Multiply the elements in each row of the left hand matrix by the corresponding elements in each column of the right hand matrix and add the results
What does multiplicatively conformable mean?
The number of columns in the first matrix equals the number of rows in the second matrix
What is the determinant of a 2x2 matrix?
ad - bc
What is a singular matrix? (2)
A matrix with a determinant of zero
It has no inverse
What is a non-singular matrix? (2)
A matrix with a determinant that is not zero
It has an inverse
What is the determinant of a 3x3 matrix?
a(minor of a) - b(minor of b) + c(minor of c)
What is the minor of an element from a 3x3 matrix?
The determinant of the 2x2 matrix that is formed when the row and column containing that element have been crossed out
What is the inverse of a matrix?
The inverse of a matrix M is M^-1 where MM^-1 = M^(-1)M = I
