Matrices Flashcards
What is the 3x3 identity matrix?
What is the 2x2 identity matrix?
What is the determinant of a matrix used for?
The area scale factor
How is the determinant of a 2x2 matrix found?
How is the determinant of a 3x3 matrix found?
What are the steps to calculate the inverse of a matrix?
1) Find the determinant
2) Find the matrix of minors
3) Find matrix of cofactors
4) Transpose matrix of cofactors
5) Divide it by the determinant (or multiply by 1/det)
What is the 2x2 rotation matrix?
What are the 3x3 rotation matrices for axis x,y and z?
Which matrices do you multiply by for a rotation anticlockwise by 90,180 and 270 degrees? (3 matrices)
Which matrices do you multiple by to reflect in x,y and z axis?
What does transposing a matrix do?
Swaps rows and columns
How do you find matrix of cofactors from the minors?
Times each value in the matrix by 1 for (+) and -1 for (-).
What is a matrix with a determinant of 0 called?
A singular matrix
What is the formula for the inverse of a 2x2 matrix?
For matrix (a,b)
(c,d), A^-1 =
What do you get if you multiply a matrix by its inverse.
Identity matrix
What is the minor of an element in a 3x3 matrix?
Determinant of the 2x2 matrix that remains after the row and column containing that element have been crossed out.
What must be true for the matrix A to be called self inverse?
A=A^-1
How many solutions does a matrix with 3D determinant of 0 have?
1 unique solution
If the 3D determinant = 0, what are the 3 possible shapes of the 3 planes and how many solutions does each have?
Sheaf - infinite solutions
Prism - no solutions
Parallel - No solutions
How can you tell that planes shown by a matrix form a prim or a sheaf.
For a sheaf, values in simultaneous equation are consistent
For a prism, values in simultaneous equation aren’t consistent
