All Flashcards
Explain matrix multiplication compatibility.
The number of columns in the first matrix must equal the number of rows in the second matrix. If A is n x m and B is m x p, they are compatible.
Explain the dot product's geometric interpretation.
The dot product relates to the angle between two vectors; it measures how much the vectors point in the same direction.
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.
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.