Matrix Multiplication Warm Up

Front

What is matrix multiplication?

Back

Matrix multiplication is a binary operation that produces a matrix from two matrices. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns'. For example, a matrix with 3 rows and 2 columns is said to have dimensions 3 x 2.

Front

Can you multiply a 2x3 matrix with a 3x2 matrix?

Back

Yes, you can multiply a 2x3 matrix with a 3x2 matrix. The resulting matrix will have dimensions 2x2.

Front

What is the result of multiplying a matrix by a zero matrix?

Back

The result of multiplying any matrix by a zero matrix is a zero matrix of appropriate dimensions.

Front

If A is a 2x3 matrix and B is a 3x4 matrix, what are the dimensions of the product AB?

Back

The dimensions of the product AB will be 2x4.

Front

What is the formula for calculating the element in the i-th row and j-th column of the product of two matrices?

Back

The element in the i-th row and j-th column of the product is calculated as the sum of the products of the corresponding elements from the i-th row of the first matrix and the j-th column of the second matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What happens when you multiply a matrix by the identity matrix?

Back

When you multiply a matrix by the identity matrix, the original matrix remains unchanged.

Front

What is a scalar multiplication of a matrix?

Back

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number).

Front

If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is AB?

Back

AB = [[1*5 + 2*7, 1*6 + 2*8], [3*5 + 4*7, 3*6 + 4*8]] = [[19, 22], [43, 50]].