# Core Pure - Matrices + Linear Transformations Flashcards

What is a square vector?

A matrix when the number of rows and columns are the same

What is an identity matrix?

A square matrix with 1’s along the principal diagonal and the rest of the elements as 0

How do you find the determinant of a 2x2 matrix?

How do you find the determinant of a 3x3 matrix?

What is a singular matrix?

A matrix where Det M = 0

How do you find the inverse of a 2x2 matrix?

What is the property of an inverse matrix?

MM⁻¹ = I

How do you find the inverse of a 3x3 matrix?

- Find the determinant of A, Det A
- Form the matrix of minors, M
- From the matrix of minors, form the matrix of cofactors, C
- Find the Transpose of the matrix of cofactors, Cᵀ
- A⁻¹ = (1/DetA) Cᵀ

What is the transpose of a matrix?

The reflection across the main diagonal

If the determinant of a matrix corresponding to 3 simultaneous equations is singular, is it consistent or inconsistent and how many solutions does it have?

If Det A = 0, the simulatanous equations may:

* Be consistnent and have infinite solutions

* Or be inconsistent and no solutions

If the determinant of a matrix corresponding to 3 simultaneous equations is non-singular, is it consistent or inconsistent and how many solutions does it have?

Is is consistant and has 1 unique solution

What is the gemoetrical representation of a matrix corresponding to 3 simultaneous equations when the determinant does NOT equal 0?

What is the gemoetrical representation of a matrix corresponding to 3 simultaneous equations when it is singular and has infinite solutions?

What is the gemoetrical representation of a matrix corresponding to 3 simultaneous equations when it is singular and has no solutions?

How do you determine whether 3 simultaneous equations with det A = 0 are consistent or inconsistent?

Form 2 equations from the 3 equatiosn (set 1 equal to x,y or z and substitute in to other 2), of the 2 formed equations are multiples of each other, it is consistent, if they are not multiples, they are inconsistent