Ti 84 Tutorial, Solve 3 by 3 System of Equations by Matrix (rref!)

TL;DR

Learn how to solve a 3x3 system of equations using matrix functions and PID, with step-by-step instructions.

Transcript

ending hi we are going to see how to solve this system of equations with the matrix function and PID for first we see that here's the matrix anything blue so we had to hit 2nd and go to matrix these are the names of the matrices but then we are going to first go to add it first and then welcome to just say that shows the first one so that we can en... Read More

Key Insights

• ❓ Matrix functions and PID are useful in solving systems of equations.
• ❓ The initial setup involves creating a 3x4 matrix with coefficients and variables.
• 🥺 The rref function simplifies the matrix, leading to the solution.
• 🤑 The diagonal elements of the rref matrix are ones, representing the variables' coefficients.
• 💁 Converting decimals to fractions helps in obtaining the final solution in fractional form.
• ❓ The solution provides values for each variable in the system of equations.
• 🤪 The X, Y, and Z columns in the rref matrix represent the respective variables.

Questions & Answers

Q: How can matrix functions and PID be used to solve a system of equations?

Matrix functions and PID are effective tools for solving systems of equations. By organizing the coefficients and variables into a matrix, we can use the rref function to obtain the solution.

Q: Why is the initial matrix setup a 3x4 matrix?

The initial setup is a 3x4 matrix because we have three unknowns and three equations. The fourth column represents the constants on the right side of the equations, making it a 3x4 matrix.

Q: What does rref stand for and what does it do?

rref stands for "row reduced echelon form." It is a function that simplifies the matrix, ensuring that the diagonals contain only ones. It displays the solution to the system of equations.

Q: How can decimals be converted to fractions?

By using the math function on the calculator and selecting the appropriate option, decimals can be converted to fractions. This helps in obtaining the final solution in fractional form.

Summary & Key Takeaways

• The content demonstrates how to solve a system of equations using matrix functions and PID.

• It explains how to set up the system of equations as a 3x4 matrix, with coefficients and variables.

• The process involves entering the matrix and using the rref function to obtain the solution.