Intro to Matrices Flashcard

Front

What is an augmented matrix?

Back

An augmented matrix is a matrix that represents a system of linear equations, including the coefficients of the variables and the constants from the equations.

Front

How do you write a system of equations as an augmented matrix?

Back

To write a system of equations as an augmented matrix, list the coefficients of the variables in each equation as rows, and include the constants as an additional column.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns', indicating how many rows and columns the matrix has.

Front

If matrix B has dimensions 3 x 2, how many rows and columns does it have?

Back

Matrix B has 3 rows and 2 columns.

Front

What does it mean for a matrix to be rectangular?

Back

A matrix is rectangular if it has a different number of rows and columns, as opposed to a square matrix which has the same number of rows and columns.

Front

What is a square matrix?

Back

A square matrix is a matrix that has the same number of rows and columns.

Front

How do you determine the dimensions of a matrix?

Back

To determine the dimensions of a matrix, count the number of rows and columns it contains.

Front

What is the significance of the augmented part of an augmented matrix?

Back

The augmented part of an augmented matrix represents the constants from the system of equations, allowing for the solution of the equations using matrix methods.

Front

What is the difference between a 2 x 3 matrix and a 3 x 2 matrix?

Back

A 2 x 3 matrix has 2 rows and 3 columns, while a 3 x 2 matrix has 3 rows and 2 columns.

Front

How can you represent the equation 2x + 3y = 5 in an augmented matrix form?

Back

The equation 2x + 3y = 5 can be represented as [2 3 | 5] in augmented matrix form.