Alg 2 sec 4.3 Flashcard (24/25)

Front

What is matrix multiplication?

Back

Matrix multiplication is an operation that produces a new matrix from two matrices by taking the dot product of rows and columns. It is only possible when the number of columns in the first matrix equals the number of rows in the second matrix.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are defined by the number of rows and columns it contains, expressed as 'rows x columns'.

Front

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

Back

No, a 2x3 matrix cannot be multiplied by a 2x2 matrix 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 2x3 matrix by a 3x2 matrix?

Back

The result is a 2x2 matrix, as the number of rows from the first matrix (2) and the number of columns from the second matrix (2) determine the dimensions of the product.

Front

What does it mean if two matrices cannot be multiplied?

Back

If two matrices cannot be multiplied, it means their dimensions are incompatible; specifically, the number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is scalar multiplication in matrices?

Back

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

Front

If a 3x2 matrix is multiplied by a 2x3 matrix, what is the dimension of the product?

Back

The product will be a 3x3 matrix.

Front

What is the dimension of the product of a 2x3 matrix and a 3x12 matrix?

Back

The product will be a 2x12 matrix.

Front

What is the result of multiplying a 1x3 matrix by a 3x1 matrix?

Back

The result will be a 1x1 matrix.

Front

If a matrix has dimensions 3x2, how many elements does it contain?

Back

It contains 6 elements (3 rows multiplied by 2 columns).