Multiplying Matrices

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers arranged in rows and columns.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form of rows x columns (e.g., a 3x2 matrix has 3 rows and 2 columns).

Front

What is scalar multiplication of a matrix?

Back

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

Front

What is the condition for matrix multiplication to be possible?

Back

Matrix multiplication is possible if the number of columns in the first matrix equals the number of rows in the second matrix.

Front

If A is a (m x n) matrix and B is a (n x p) matrix, what are the dimensions of the product AB?

Back

The dimensions of the product AB will be (m x p).

Front

What is the result of adding two matrices?

Back

The result of adding two matrices is a new matrix where each element is the sum of the corresponding elements of the original matrices.

Front

What is the result of subtracting two matrices?

Back

The result of subtracting two matrices is a new matrix where each element is the difference of the corresponding elements of the original matrices.

Front

What is the product of a (2x3) matrix and a (3x2) matrix?

Back

The product will be a (2x2) matrix.

Front

What happens if you try to multiply a (3x2) matrix by a (2x3) matrix?

Back

The product will be a (3x3) matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.