Dimensions of matrices involved in operations must match.
Here is a short summary
You can only add and subtract matrices that have the same dimensions: the numbers of rows must be equal, and the number of columns must be equal.
The multiplication of structured mathematical entities (vectors, complex
numbers, matrices, etc.) is different from the multiplication of
unstructured (scalar) mathematical entities (regular umbers). As you
well know matrix multiplication is not commutative> This has to do
with the dimensions.
An mXn matrix has m rows and
n columns. To perform multiplication of an kXl matrix by
an mXn matrix you multiply each element in one row of the first
matrix by a specific element in a column of the second matrix. This
imposes a condition, namely that the number of columns of the first
matrix be equal to the number of rows of the second.
Thus, to be
able to multiply a kXl matrix by am mXn matrix, the number of columns of
the first (l) must be equal to the number of rows of the second (m).
Let there be two matrices MatA and MatB. The dimensions are indicated as mXn where m and n are natural numbers (1,2,3...)
The product MatA(kXl) * MatB(mXn) is possible only if l=m
MatA(kX3) *
MatB(3Xn) is possible and meaningful, but
MatA(kX3) * MatB(nX3) may not
be possible.
To get back to your calculation, make sure that the
number of columns of the first matrix is equal to the number of rows of
the second. If this condition is not satisfied, the calculator
returns a dimension error. The order of the matrices in the
multiplication is, shall we say, vital.
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