sheldonrocks97 said:Homework Statement
Find nonzero matrices A; B; C such that AC = BC
and A does not equal B
Homework Equations
None that I know about.
The Attempt at a Solution
I'm not sure where to start, I would like to know how to complete this problem.
A nonzero matrix is a matrix that contains at least one nonzero element. This means that it is not a matrix full of zeros.
Two matrices are considered equal if they have the same dimensions and all corresponding elements are equal. In other words, they have the same number of rows and columns, and each element in the same position in both matrices has the same value.
Yes, it is possible for two matrices A and B to have the same product AB, but for A and B to be different matrices. This is because matrix multiplication depends on the dimensions of the matrices, not just their values.
Yes, it is possible for two matrices A and B to be different, but for their products with another matrix C to be equal. This can happen if the matrices have the same number of columns, but different number of rows.
Nonzero matrices with equal products are useful for solving equations and systems of equations. By using matrix multiplication, we can find values for the matrices that satisfy the equation or system, even if the matrices themselves are not equal.