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Physicsissuef
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Homework Statement
I have two 3x3 matrices A and B
and my problem is to find XA=B and AY=B
Isn't XA=B and AY=B
Homework Equations
The Attempt at a Solution
[tex]X=A^-^1 B[/tex]
[tex]Y=A^-^1 B[/tex]
or I am wrong?
malawi_glenn said:remember that matrix multiplication is non-commutative
so yes you are wrong on the [tex]X=A^-^1 B[/tex], if XA=B
D H said:You can pre- or post-multiply a matrix equality by a matrix to yield another matrix equality: If A=B then CA = CB and AD = BD for all matrices C, D of the correct dimensionality. Use this plus the fact that matrix multiplication is associative to find a form that eliminates the matrix A from XA=B.
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
The X and Y solutions refer to the values of the variables in the equations XA=B and AY=B that make the equations true.
To solve equations using matrices, you can use techniques such as Gaussian elimination, matrix inversion, or Cramer's rule. These techniques involve manipulating the matrix equations to isolate the variables and find their values.
Yes, matrices can be used to solve many real-world problems in various fields such as engineering, physics, economics, and computer science. They can be used to model and analyze complex systems and relationships between variables.
Some common applications of matrix solutions for equations XA=B and AY=B include solving systems of linear equations, finding the inverse of a matrix, and solving optimization problems. They are also used in computer graphics, data analysis, and machine learning algorithms.