1.2_Matrix Multiplication

Front

What is matrix multiplication?

Back

Matrix multiplication is an operation that takes two matrices and produces a third matrix by multiplying rows of the first matrix by columns of the second matrix.

Front

What are the conditions for two matrices to be multiplied?

Back

Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Front

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

Back

The dimension of the product AB will be 2x4.

Front

Can a 2x2 matrix be multiplied by a 2x3 matrix?

Back

Yes, a 2x2 matrix can be multiplied by a 2x3 matrix.

Front

What is the dimension of the product of a 3x2 matrix and a 2x5 matrix?

Back

The dimension of the product will be 3x5.

Front

If matrix A is 2x3 and matrix B is 3x2, what is the dimension of the product AB?

Back

The dimension of the product AB will be 2x2.

Front

What happens if you try to multiply a 2x3 matrix by a 2x2 matrix?

Back

The multiplication is not possible because the number of columns in the first matrix (3) does not equal the number of rows in the second matrix (2).

Front

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

Back

Multiplying any matrix by the identity matrix of compatible dimensions results in the original matrix.

Front

If matrix A is 4x2 and matrix B is 2x3, what is the product AB?

Back

The product AB will be a 4x3 matrix.

Front

What is the zero matrix?

Back

The zero matrix is a matrix in which all elements are zero. It acts as the additive identity in matrix addition.