Answer:
AX is not the same as AE.
Step-by-step explanation:
Symbols and Variables:
Let
A be a matrix.
Let
X and
E be matrices or vectors of appropriate dimensions.
Understanding
AX:
AX represents the product of matrix
A and matrix/vector
X.
This product follows the rules of matrix multiplication, where the number of columns in
A must match the number of rows in
X.
Understanding
AE:
Similarly,
AE represents the product of matrix
A and matrix/vector
E.
This product follows the same rules of matrix multiplication, where the number of columns in
A must match the number of rows in
E.
Equating
AX and
AE:
For
AX to be the same as
AE,
X and
E must be identical.
This means that
=
X=E.
General Case:
Unless it is explicitly given that
X and
E are the same matrix/vector, we cannot assume
AX is the same as
AE.
Thus, AX is not the same as AE unless
=
X=E.
