How to do matrix multiplication
post is rather exhaustive as regards the matrix capabilities of the
calculator. So if the post recalls things you already know, please skip
them. Matrix multiplication is at the end.
Let me explain how to create matrices. (If you know how to do it, skip
to the operations on matrices, at the end.)
First you must set
[MODE][6:Matrix]. Then By entering one of the numbers [1:MatA] or
[2:Matb] or [3:MatC] you get to choose the dimensions of the matrix
(mxn]. Once finished entering the matrix you clear the screen.
The operations on matrices are available by pressing [Shift][Matrix]
[1:Dim] to change the dimension of a matrix (in fact redefining the
[2:Data] enter values
in a matrix
[3:MatA] access Matrix A
[4:Matb] access Matrix B
[5:MatC] access matrix C
[6:MatAns] access the Answer Matrix (the last matrix calculated)
[7:det] Calculate the determinant of a matrix already defined
[8:Trn] The transpose of a matrix already defined
To add matrices MatA+MatB (MUST have identical dimensions same m and same n, m and n do not have to be the same)
To subtract MatA-MatB. (MUST have identical dimensions, see above)
To multiply MatAxMatB (See below for conditions on dimensions)
To raise a matrix to a power 2 [x2], cube [x3]
To obtain inverse of a SQUARE MatA already defined MatA[x-1]. The key [x-1] is the x to
the power -1 key. If the determinant of a matrix is zero, the matrix is singular and its inverse does not exit.
Dimensions of matrices involved in operations must match. Here is a
The multiplication of structured mathematical
entities (vectors, complex
numbers, matrices, etc.) is different from the multiplication of
unstructured (scalar) mathematical entities (regular numbers). 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).
MatA(kXl) * MatB(mXn) is possible only if l=m
Mat(3Xn) is possible and meaningful, but
Mat(kX3) * Mat(nX3) may not
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.
Jan 09, 2011 |
Casio FX-115ES Scientific Calculator