Matrices to Solve 3 Simultaneous Equations | Manually & with Python
Learn how to solve a system of 3 simultaneous equations using matrices, with a pen and paper and with Python! In this video you will learn how to setup and solve matrix equations using exam-friendly pen and paper methods as well as how to use a Python library to solve the same problem. You will see how matrix equations are solved in the real world where pen and paper methods are too tedious and time-consuming.
#maths #matrices #python
You will learn step-by-step:
How to convert a system of 3 linear equations to a matrix equation
What definitions of matrix equations to use
How to evaluate the determinant of a 3x3 matrix
How to find the matrix of cofactors (adjoint) of a 3x3 matrix
How to find the inverse of a 3x3 matrix using its determinant and matrix of cofactors
How to solve for a vector of unknowns to find the required solution for simultaneous equations
How to import the required library inside of Python
How to define matrices using the Sympy Python library
How to find the vector of unknowns using Python computation
Chapter breakdown:
00:00 - Introduction to the problem
00:21 - What does it mean to solve a system of linear equations?
00:49 - Turning our 3 equations into one matrix equation
01:03 - Writing out our transformation matrix A, unknown vector u and constant vector k
02:28 - Inverting (rearranging) our equation for the unknown vector
03:22 - The formula for finding the inverse of a 3x3 non-singular matrix
04:06 - Finding the determinant of our matrix
08:12 - Finding and transposing the matrix of cofactors (adjoint)
11:55 - Finding the final values for x, y and z
14:45 - Looking at computational methods
15:05 - Importing the Sympy Python library
15:50 - Defining our matrix A and vector of constants k
16:53 - Previewing our matrix A in Python
17:08 - Solving our equation in 3 lines of Python code!
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matrices, matrix algebra, simultaneous equations, mathematics, physics, data science, artificial intelligence, machine learning, python, programming
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