Lesson 3-2 Practice

Front

What are the conditions for two matrices to be multiplied?

Back

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

Front

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

Back

The product AB will be a 2x4 matrix.

Front

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

Back

The product will be a 3x5 matrix.

Front

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

Back

The product AB will be a 4x3 matrix.

Front

What happens if you try to multiply a 3x4 matrix by a 3x2 matrix?

Back

The multiplication is undefined because the number of columns in the first matrix does not equal the number of rows in the second matrix.

Front

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

Back

The product AB will be a 2x2 matrix.

Front

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

Back

The result is the original matrix, as the identity matrix acts as a multiplicative identity.

Front

If matrix A is 3x3 and matrix B is 3x3, what is the maximum number of non-zero entries in the product AB?

Back

The maximum number of non-zero entries in the product AB can be 9, assuming both matrices are full rank.

Front

What is the definition of a zero matrix?

Back

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

Front

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

Back

The product AB will be a 2x2 matrix.