There is no point reaching for a calculator that cannot show its working. This one starts from a1, a2, a3, b1, b2, b3, c1, c2, c3, x1, x2, x3, y1, y2, y3, z1, z2, z3 and one way and reports c11, c12 and c13, so you can see how each answer follows from the numbers you entered.
What Is the Matrix Multiplication Calculator?
The matrix multiplication calculator works through a1, a2, a3, b1, b2, b3, c1, c2, c3, x1, x2, x3, y1, y2, y3, z1, z2, z3 and one way to give you c11, c12 and c13.
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Matrix Multiplication Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with a1 set to 10, a2 set to 5, a3 set to 2, the calculator returns c11 of 50, and c11 (c11 2) of 100, and c11 (c11 3) of 300. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out c11?
Enter a1, a2, a3, b1, b2, b3, c1, c2, c3, x1, x2, x3, y1, y2, y3, z1, z2, z3 and one way. The calculator then works through the relationship and reports c11, c12 and c13.
What does the matrix multiplication actually calculate?
It takes a1, a2, a3, b1, b2, b3, c1, c2, c3, x1, x2, x3, y1, y2, y3, z1, z2, z3 and one way and converts them into c11, c12 and c13 using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter a1?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.