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−1
X = A
B.
So if you are able to perform the inverse of matrix and able to multiply matrices you can solve a linear
system without needing to learn another calculator's function.
What about complex matrices? You cannot enter complex numbers in a normal matrix. You have to
create a complex matrix first. The procedure to do this is like that of creating a complex number. First
you enter the real part, then you enter the imaginary part and then you press
As here it is not a normal sum but a matrix sum we have to enter two matrices of the same size. In
fact one can create an empty complex matrix and then edit it. For example, to create a 3x3 complex
matrix we do (with the MATRIX menu active)
3 ENTER NEW ENTER
where '3 ENTER' puts the number 3 in register x and register y of the stack. 'NEW' creates a 3x3 real
matrix. 'ENTER' creates another one and ' COMPLEX' makes the complex matrix.
We are not going to study the second and the third line of the
there are two functions in the second line that may be useful. They are: DOT and CROSS. As you
know vectors can be represented by a single row or a single column matrix. In the HP-42S, vectors
will be represented only by single row matrices.
There is nothing special to say about addition, subtraction or multiplication by a scalar since there is
no difference for the case of a matrix. But if you want to calculate the dot product in the calculator
you can use DOT function. As you know if we have two vectors A and B, the dot product is
A
B
+A
B
+A
B
. If the number of dimensions is not 3 but N we calculate the dot product in the same
x
x
y
y
z
z
B
B
B
way as A
B
+...+A
B
1
1
N
B
spend a lot of time just to enter the vector in the calculator).
The cross product which is given by i(A
interesting and can be calculated using the CROSS function. The cross product is only defined in 3
dimensions.
Example: Calculate A×B for A = 5i + 3j – 2k and B = i – 5k.
Solution: '×' usually means cross product while '●' usually means dot product.
Let's enter the vector A.
MATRIX
1 ENTER 3 NEW
EDIT 5 ENTER → 3 ENTER → 2 +/– ENTER EXIT STO "A"
(In fact we don't need the ENTER)
Let's enter now the vector B.
1 ENTER 3 NEW
EDIT 1 ENTER → → 5 +/– ENTER EXIT STO "B"
We have stored both matrices because when you use the EDIT function, if you press ENTER as we
did, what you enter goes onto to the stack and we would lose the first matrix.
COMPLEX
. You probably won't use this because it is faster to do by hand! (we would
N
B
B
–A
y
z
B
MATRIX
B
) + j(A
B
–A
B
) + k(A
z
y
z
x
x
z
B
B
B
COMPLEX.
menu (too specialized) but
B
–A
B
) is more
x
y
y
x
B
B
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