I'd first like an explanation of WHY matrices are used. How is the solution used?? Arithmetic, algebra, geometry, trigonometry, calculus, statistics... are all fairly self-explanatory. Before you need to know how to multiply matrices, you need to know why you would do so.
Am I right in thinking that multiplication of matrices is non-commutative. ie, [matrix a][matrix b] yields a different result from [matrix b][matrix a]? Or is there some rule that determines the order they should be placed in? My memory of matrices from schoolwork is almost completely gone. Only the memory of slogging through seemingly endless series of rough-book calculations remains.
@@erniemorris9991 What do you mean by "unless all values(elements) in a matrix are the same"? Suppose A and B are 2x2 matrices and B is the inverse of A. Then A*B and B*A are equal to the unit matrix. No need that the elements in A and B "are the same".
Matrix multiplication is part of linear algebra. Matrix operations simplify mathematics on combinations of vectors. Nearly all of the programming that I did during my years in computer-aided design and manufacturing was based on linear algebra and matrix operations.
I'd first like an explanation of WHY matrices are used. How is the solution used?? Arithmetic, algebra, geometry, trigonometry, calculus, statistics... are all fairly self-explanatory. Before you need to know how to multiply matrices, you need to know why you would do so.
You would use this in changing the basis in a vector space or tensor product space. Watch 3Blue1Brown's Linear Algebra series.
@@robertbrandywine I recently learned that a more practical use is solving multiple variable linear equations.
Am I right in thinking that multiplication of matrices is non-commutative. ie, [matrix a][matrix b] yields a different result from [matrix b][matrix a]? Or is there some rule that determines the order they should be placed in?
My memory of matrices from schoolwork is almost completely gone. Only the memory of slogging through seemingly endless series of rough-book calculations remains.
@@erniemorris9991 What do you mean by "unless all values(elements) in a matrix are the same"? Suppose A and B are 2x2 matrices and B is the inverse of A. Then A*B and B*A are equal to the unit matrix. No need that the elements in A and B "are the same".
Takes me back to school. I'd totally forgotten about operating with matrices. But then, I am 64! Thanks! 👍
We touched on matrices briefly in school. It seemed that even the teacher didn't know how these things were useful.
Great lesson i just remember how to solve the matrix !!!
The question is why would you want to do this?
Matrix multiplication is part of linear algebra. Matrix operations simplify mathematics on combinations of vectors. Nearly all of the programming that I did during my years in computer-aided design and manufacturing was based on linear algebra and matrix operations.