Matrices Flashcards
What is a matrix?
A table of values
What is meant by the order of a matrix?
The number of rows and columns.
When determining the order of a matrix, are the rows or columns looked at first?
Rows, then columns
What is an element in a matrix?
An individual term
What is a square matrix?
Matrices with the same number of rows and columns (2x2, 3x3, 4x4, etc)
What is meant by matrices being non-conformable under addition?
You can’t add or subtract matrices of different orders
How do you multiply a matrix by a scalar?
Multiply each element within the matrix by the scalar
What is the identity matrix?
A matrix with 1 down the diagonal and the rest 0
What is meant by associativity?
(xy) * z = x * (yz)
What is meant by commutativity?
xy = yx
Is matrix addition associative?
Yes
Is matrix subtraction associative?
No
Is matrix addition commutative?
Yes
Is matrix subtraction commutative?
No
Is matrix multiplication commutative?
No
In order to multiply 2 matrices, what must the form be?
( a x n) x (n x b)
What order will the resulting matrix of ( a x n) x (n x b) be?
a x b
Is matrix multiplication associative?
Yes
What is meant by matrix multiplication being distributive?
A(B+C) = AB+AC
What is the general form for a rotation transformation matrix?
(cos x -sin x)
(sin x cos x)`
What is a shear?
Each point in one axis is moved by a multiple of its other axis
What is the general matrix for a shear parallel to the x-axis?
(1 a)
(0 1)
What is the general matrix for a shear parallel to the y-axis?
(1 0)
(b 1)
How would you describe a shear?
A shear of factor z, x/y-axis invariant, where the point (a,b) is mapped to (c,d)
How do you combine matrix transformations?
Transformation A followed by transformation B is the same as applying BA
How would you find invariant points with matrices?
Put it in the form: (a b)(x) = (x)
(c d)(y) = (y)
Then form equations and simplify
