Chapter 1 Matrices And Transformations Flashcards
What is a matrix?
A matrix is a rectangular array of numbers or letters.
What describes the shape of a matrix?
The shape of a matrix is described by its order, which is defined by the number of rows and columns.
What is the order of a matrix with r rows and c columns?
The order of a matrix with r rows and c columns is r x c.
What is a square matrix?
A matrix with the same number of rows and columns is called a square matrix.
What is an identity matrix?
A matrix of the form I is known as an identity matrix. All identity matrices are square, with 1s on the leading diagonal and zeros elsewhere.
What is a zero matrix?
The matrix 0 is known as the zero matrix. Zero matrices can be of any order.
When can two matrices A and B be multiplied?
Two matrices A and B can be multiplied to give matrix AB if their orders are p x q and q x r respectively.
The resulting matrix will have the order p x r
When can matrices be added or subtracted?
Matrices can be added or subtracted if they have the same order.
What is the associative property of matrix addition?
A + (B + C) = (A + B) + C
What is the associative property of matrix multiplication?
A(BC) = (AB)C
Is matrix addition commutative?
Yes, A + B = B + A
Is matrix multiplication commutative?
No, AB ≠ BA
What does the matrix
M = [a b
c d]
represent?
It represents the transformation that maps a point with position vector
[x
y]
to another point with position vector [ ax + by
cx + dy ]
What types of transformations are represented by matrices?
Common transformations include rotations, reflections, enlargements, stretches, and shears.
What is the composite transformation of M followed by N?
It is represented by the matrix product NM.
What is an invariant point under a transformation?
If (x, y) is an invariant point, it remains unchanged under the transformation represented by the matrix.
What is an invariant line under a transformation?
A line AB is known as an invariant line if the image of every point on AB is also on AB.
