Csmath2 Flashcards
(31 cards)
Matrix is what type of array
Rectangular array
What is the number of rows by the number of columns
Size/dimension of matrix
Inside the matrix is called
Entries/elements
Consider matrix A of size mxn , if m = n, what type of matrix is this?
Square matrix of order n
(3x3 can just be said as 3)
Size mxn, if m = 1, then A is a ____
Row matrix
Size mxn, if n = 1, then A is a ____
Column matrix
When are matrices A and B equal?
- If size of A and B are the same
- if entries/elements of A and B are the same
Condition for matrix addition
Matrices must have the same size
What is the sum of matrices with different size?
Undefined
Properties of matrix addition
Commutative: A+B = B+A
Associative:
(A+B)+C = A+(B+C) = (C+B)+A
Scalars are what type of numbers?
All real numbers
Requirement for subtracting A and B
-A n B must have same size
What represents A-B?
Sum of A and (-1)B
Properties of subtraction
-NOT commutative: A-B ISNT B-A
-NOT associative: (A-B)-C ISNT A-(B-C)
For any matrix A, there is a unique matrix, such that if you add A and this matrix together, it is equal to A
Zero matrix/additive identity (O)
For each A, there is a unique B where A+B = O
Additive inverse
B = additive inverse of A
Or scalar multiple of -1
Properties of scalar multiplication
-associative: (rs)A = r(sA)
r and s are scalars
-distributive: r(A+B) = rA + rB
(r+s)A = rA + sA
Are O matrix unique for every dimension?
Yes, there’s only 1 O matrix for every nxn matrix
Requirement for distributive property of scalar multiple
A and B must be of equal size
r(A+B) = rA + rB
Properties of Mult matrices
-NOT commutative: AxB ISNT BxA
-IS associative: Ax(BxC) = (AxB)xC
-distributive: (A+B)C = AC + BC
Requirements for AxB
of Columns of A must be the same as the # of rows of B
Size of AxB
row of A by column of B
(rA)B = r(AB) = A(rB)
True
If A is an mxn matrix, the transpose of A is?
an nxm matrix
