Add/Subtract/Scalar Multiplication/Dimensions of Matrices

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

How do you add two matrices?

Back

To add two matrices, they must have the same dimensions. You add corresponding elements from each matrix.

Front

What is scalar multiplication of a matrix?

Back

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

Front

What must be true 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

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

Back

The result will be a 2x2 matrix.

Front

If matrix A is 3x2 and matrix B is 2x4, what are the dimensions of the product AB?

Back

The dimensions of the product AB will be 3x4.

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero. It serves as the additive identity in matrix addition.

Front

How do you determine if two matrices are equal?

Back

Two matrices are equal if they have the same dimensions and all corresponding elements are equal.

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 about the matrix.