Flashcard Week 15

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 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 2x3 and matrix B is 3x2, what is the size of the resulting matrix when A is multiplied by B?

Back

The resulting matrix will be 2x2.

Front

What happens if the dimensions of two matrices are not compatible for multiplication?

Back

If the dimensions are not compatible, the matrices cannot be multiplied, and the operation is undefined.

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

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

Can matrix multiplication be performed in any order?

Back

No, matrix multiplication is not commutative; that is, A*B does not necessarily equal B*A.

Front

What is the associative property of matrix multiplication?

Back

The associative property states that (A*B)*C = A*(B*C) for any matrices A, B, and C where the multiplication is defined.

Front

What is a zero matrix?

Back

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

Front

How do you calculate the element in the i-th row and j-th column of the product of two matrices?

Back

To find the element in the i-th row and j-th column of the product, take the dot product of the i-th row of the first matrix and the j-th column of the second matrix.