Adding, Subtracting, and Multiplying by Scalars Matrices

Front

What is a scalar in relation to matrices?

Back

A scalar is a single number that can multiply a matrix, affecting each element of the matrix by that number.

Front

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. You add corresponding elements together.

Front

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

Back

Each element of the matrix is multiplied by the scalar.

Front

What is the dimension of a matrix?

Back

The dimension of a matrix is defined by the number of rows and columns it has, expressed as 'rows x columns'.

Front

Can you subtract two matrices of different dimensions?

Back

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

Front

What is the formula for matrix addition?

Back

If A and B are two matrices of the same dimension, then A + B = [a_{ij} + b_{ij}] for all i,j.

Front

What happens if you try to add a 2x3 matrix and a 3x2 matrix?

Back

You cannot add them because their dimensions are not the same.

Front

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

Back

The result is a 2x2 matrix.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, denoted as I.

Front

What is the determinant of a matrix?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix, providing important properties of the matrix.