All Flashcards
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.
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 determine if two matrices can be multiplied?
Check if the number of columns in the first matrix equals the number of rows in the second matrix.
How do you find the element in the ith row and jth column of the product of two matrices?
Calculate the dot product of the ith row of the first matrix and the jth column of the second matrix.
Given A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], find the element in the first row and first column of AB.
Multiply the first row of A by the first column of B: (15) + (27) = 5 + 14 = 19.