All Flashcards
What is a matrix?
A rectangular array of numbers, symbols, or expressions arranged in rows and columns.
What are matrix dimensions?
The number of rows and columns in a matrix, expressed as n x m (rows x columns).
What is the dot product of two vectors?
The sum of the products of corresponding components of two vectors, resulting in a scalar.
Define matrix compatibility in multiplication.
For matrices A and B, the number of columns in A must equal the number of rows in B for multiplication to be possible.
How do you calculate the dot product of vectors A and B?
If A = [a1, a2] and B = [b1, b2], then A • B = a1b1 + a2b2.
If matrix A is n x m and matrix B is m x p, what are the dimensions of matrix C = A x B?
C is an n x p matrix.
Is matrix multiplication commutative? Explain.
No, matrix multiplication is generally not commutative. AB is not necessarily equal to BA.