Matrices & Systems of Linear Equations

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, 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 the number of columns.

Front

What is an augmented matrix?

Back

An augmented matrix is a matrix that includes the coefficients of a system of linear equations along with the constants from the equations.

Front

How do you represent a system of linear equations using matrices?

Back

A system of linear equations can be represented using a coefficient matrix and a constant matrix, often written in the form AX = B.

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if there is at least one solution that satisfies all equations in the system.

Front

What does it mean for a system of equations to be inconsistent?

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A system of equations is inconsistent if there are no solutions that satisfy all equations in the system.

Front

What is the solution to a system of linear equations?

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The solution to a system of linear equations is the set of values for the variables that make all equations true.

Front

What is the Gaussian elimination method?

Back

Gaussian elimination is a method for solving systems of linear equations by transforming the system into an upper triangular form.

Front

What is a determinant?

Back

The determinant is a scalar value that can be computed from the elements of a square matrix, providing information about the matrix's properties, such as whether it is invertible.

Front

What is the 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.