Chapter 6- Matrices Flashcards
What is a square matrix?
A matrix where the number of rows and columns are the same.
What is a zero matrix?
A matrix in which all elements are 0, denoted by 0.
What is an identity matrix?
A square matrix in which the elements on the leading diagonal (start top left) are 1 and the rest are 0.
Denoted by I (subscript) k, where k describes the size.
How do you denote the size of a matrix?
n x m
n: number of rows
m: number of columns
When can matrices be multiplied together?
When the number of columns of the first matrix is equal to the number of rows in the second matrix.
How do you find the determinant of a
2x2 matrix?
ad-bc
What does the determinant show?
If detM=0, M is a singular matrix.
If detM does not equal 0, M is a non singular matrix.
How do you find the determinant of a 3x3 matrix?
a (a’s minor) - b (b’s minor) + c (c’s minor)
What is the minor of an element in a 3x3?
The determinant of the 2x2 matrix left when the row and column with that element are crossed out.
How do you find the inverse of a 2x2 matrix?
(1/detM) (d -b)
(-c a)
If A and B are non singular matrices, what does (AB)-1 equal?
(AB)-1 = A-1 B-1
Which matrices don’t have inverses?
Singular matrices as detM=0 and 1/detM = 1/0 which is undefined.
What are the steps to invert a 3x3 matrix?
-Form the matrix of minors
-Form the matrix of cofactors + and - (using minors)
-Form the transpose (swap rows and columns) of the matrix of cofactors
-Multiply by 1/detA (first matrix)
What does it mean if a system of linear equations are consistent?
There is at least one set of values that satisfies all equations simultaneously (all cross at one or infinite points).
Otherwise it is inconsistent.
What is the geometrical configuration of the planes corresponding to a non-singular matrix?
Planes meet at one point.
