Matrix Operations and Multiplication

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What does it mean to add two matrices?

Back

To add two matrices, they must have the same dimensions, and you add corresponding elements.

Front

What is the result of adding the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]]

Front

What is matrix multiplication?

Back

Matrix multiplication involves taking the dot product of rows and columns from two matrices.

Front

What are the conditions for multiplying two matrices?

Back

The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

If A is a 2x3 matrix, what dimensions can the matrix B have for multiplication?

Back

Matrix B must be a 3xN matrix, where N can be any positive integer.

Front

What is the product of the matrices A = [[1, 2, 3], [4, 5, 6]] and B = [[7, 8], [9, 10], [11, 12]]?

Back

A * B = [[1*7 + 2*9 + 3*11, 1*8 + 2*10 + 3*12], [4*7 + 5*9 + 6*11, 4*8 + 5*10 + 6*12]] = [[58, 64], [139, 154]]

Front

What is the identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

What is the zero matrix?

Back

A zero matrix is a matrix in which all elements are zero.

Front

How do you subtract two matrices?

Back

To subtract two matrices, they must have the same dimensions, and you subtract corresponding elements.