Matrices (addition, subtraction, scalars)

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 'rows x columns', indicating the number of rows and columns.

Front

Can you add two matrices of different dimensions?

Back

No, you cannot add two matrices unless they have the same dimensions.

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 is a 2x3 matrix and B is a 2x3 matrix, what is the result of A + B?

Back

The result is also a 2x3 matrix, obtained by adding corresponding elements.

Front

What happens if you try to subtract a 3x2 matrix from a 2x3 matrix?

Back

The operation is not possible because the matrices have different dimensions.

Front

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

Back

Each element of the matrix is multiplied by the scalar, resulting in a new matrix of the same dimensions.

Front

If matrix A has dimensions 3x4, how many elements does it have?

Back

It has 12 elements (3 rows x 4 columns).

Front

What is the identity matrix?

Back

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

Front

How do you determine if two matrices can be added?

Back

Two matrices can be added if they have the same dimensions.