Test: Matrices Algebraic Reasoning

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Front

What does it mean to multiply a matrix by a scalar?

Back

Multiplying a matrix by a scalar means to multiply every element of the matrix by that scalar value.

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 difference between two matrices?

Back

The difference between two matrices is found by subtracting corresponding elements of the second matrix from the first.

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 a multiplicative identity in matrix multiplication.

Front

What is a zero matrix?

Back

A zero matrix is a matrix in which all elements are zero.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in terms of rows and columns, expressed as 'm x n' where m is the number of rows and n is the number of columns.

Front

What is a transpose of a matrix?

Back

The transpose of a matrix is obtained by swapping its rows with its columns.

Front

What is a determinant?

Back

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

Front

What is an inverse of a matrix?

Back

The inverse of a matrix A is another matrix, denoted A^-1, such that when A is multiplied by A^-1, the result is the identity matrix.