what the heck is a matrice equation? and why wasnt i taught this in high school. I instantly hate math 102
2x + 3y + 4z = 5
2x - y + 2z = 3
5x + 2y - z = 8
the matrix equation for this would be :
⎡2 3 4⎤⎡x⎤.. ⎡5⎤
⎜2-1 2⎜⎜y⎜= ⎜3⎟
⎣5 2-1⎦⎜z⎟..⎣8⎦
(Hard to line up nicely)
At this point it is essential that you learn matrix multiplication.
Also learn about "inverse matrix" and how to find it
I watched a video on that. I kinda understand what they were doing. I believe must of it was simple multiplication. My instructor said we wont use this much in math 102. Maybe two or three questions on a test. But that's about it. With that being said I must get as much info as possible since this is a whole new system I never learned.
A matrix equation is an equation that involves matrices. A matrix is a rectangular array of numbers or variables, arranged in rows and columns. It's used in various branches of mathematics, including linear algebra.
In a matrix equation, you have a matrix on the left-hand side, a matrix on the right-hand side, and an equal sign in the middle. The goal is to find the values of the variables or unknowns that make the equation true.
For example, consider the following matrix equation:
A * X = B
In this equation, A and B are matrices, X is a matrix of unknowns, and the "*" symbol represents matrix multiplication.
To solve this equation, you need to perform matrix operations. Start by finding the inverse of matrix A, denoted as A^(-1). Then multiply both sides of the equation by A^(-1):
A^(-1) * (A * X) = A^(-1) * B
Since matrix multiplication is associative, you can simplify the left-hand side:
(A^(-1) * A) * X = A^(-1) * B
The product of a matrix and its inverse is the identity matrix, denoted as I:
I * X = A^(-1) * B
Multiplying any matrix by the identity matrix leaves the matrix unchanged. Therefore:
X = A^(-1) * B
Now, you can calculate the value of X by multiplying the inverse of matrix A by matrix B.
Matrix equations are an important concept in linear algebra and are used in various applications, such as solving systems of linear equations, transforming geometric objects, and more advanced mathematical concepts.
As for why you may not have been taught this in high school, the curriculum varies from school to school and country to country. Some schools may cover matrix equations in more advanced math courses or in specialized math tracks. It's also possible that it was not included in your particular curriculum. It's important to remember that math is a vast subject, and what you learn in high school is just a fraction of what is out there. If you're feeling overwhelmed or frustrated, it might be helpful to seek additional resources or support to better understand the topics. Math can be challenging, but with the right approach and resources, it can become more manageable and even enjoyable.