Matrix Equations and Their Solutions

This video tutorial demonstrates how to use the Desmos matrix calculator to solve a system of two linear equations with two unknowns using a matrix equation. It covers forming the matrix equation, solving for the variable matrix using the inverse of the coefficient matrix, and verifying the solution by substituting the results back into the original equations. The tutorial also provides step-by-step instructions for entering matrices into the Desmos calculator and converting results to fraction form.

What is the primary tool used in this video to solve the system of equations?

• Spreadsheet software

• Scientific calculator

• Desmos matrix calculator

• Graphing calculator

In the matrix equation, what does the first row of the coefficient matrix represent?

• The constants from the equations

• The coefficients of x and y from the first equation

• The variables x and y

• The solution to the system

What is the purpose of finding the inverse of the coefficient matrix?

• To check if the system has no solution

• To determine the determinant of the matrix

• To simplify the constant matrix

• To solve for the variable matrix

What is the result of multiplying a matrix by its inverse?

• Variable matrix

• Identity matrix

• Zero matrix

• Constant matrix

Which button on the Desmos calculator converts decimal approximations to fractions?

• Clear all

• New matrix

• Convert to fraction

• Identity matrix

What are the elements of the solution matrix x in fraction form?

• 17/11 and 13/22

• 7 and 5

• 3 and 4

• 4 and -2

What does it mean if a system of equations is consistent and independent?

• It has a dependent solution

• It has exactly one solution

• It has infinitely many solutions

• It has no solution

How do you verify the solution of the system of equations?

• By checking the inverse of the matrix

• By finding the determinant of the matrix

• By substituting the solution back into the original equations

• By graphing the equations

What should the result be when substituting the solution back into the first equation?

• 13/22

• 7

• 0

• 5

What error was corrected during the verification of the second equation?

• Wrong constant value

• Mistake in the variable matrix

• Error in the denominator

• Incorrect coefficient of x