[?] Multiply a 2x2 matrix with a vector?

Questions
1

I’m still a newcomer, studying matrices which I’ve never had.

I have the following equation:

m = {{11, 1}, {0, -6}};
MatrixForm {m}

I get this result:

{{{11 MatrixForm, MatrixForm}, {0, -6 MatrixForm}}}

Where did the 1 go? This is a 2x2 matrix which I wish to multiply a vector with. I assume (right or wrong?) that I use the dot operator. However, without the 1, I do not get the correct result. And I don’t understand why the function name shows up. I know the detail shows it should use a list, I’m assuming (right or wrong again?) that using the variable name would suffice.

I’ve gone over the tutorial many many times to no avail. Am I using the function MatrixForm incorrectly?

Obviously, I’m missing something simple, but I don’t know what…

Tim

2

MatrixForm {m} means "multiply MatrixForm by a list containing m.

You probably intended MatrixForm[m].

3

Hi Timothy,

Not sure which tutorial you were following, this one has several examples of matrix and vector multiplication.

4

That was it…

Now if I multiply that by vector a which is (-4,2) I get a result of {-44, -16}, the correct answer is {-42, -12} and I don’t understand why I get the wrong one…

I even worked it by hand to make sure the indicated correct answer is indeed the correct answer.
That is using the dot operator.
I’ve literally been looking at this for weeks.

Tim

5

Yes, that is the one I have been going over multiple times.

Now can you take a look at my other response of why the wrong answer comes out when I use the vector with a dot operator times the matrix?

Tim

6

m = {{11, 1}, {0, -6}};
m.{-4, 2}

(* {-42, -12} *)
7

Rohit,
Can you explain what you did to get the correct answer? Have I not gone far enough in the tutorial?
Learning curve on this is quite steep at 65…

Tim

8

Did I put in the wrong order? I should use matrix multiplied by vector instead?
Gotta run back upstairs now and try that…

Whew!

Tim

9

Hi Tim,

I did exactly what is in my reply.

Set m to {{11, 1}, {0, -6}}

m = {{11, 1}, {0, -6}};

Take the dot product of m with {-4, 2}

m.{-4, 2}

Do you not get the right answer if you copy and paste those two lines into a notebook and evaluate them?

10

It shows me that a vector multiplied by a matrix is not the same as a matrix multiplied by a vector. Dang, so simple…

Thank you so very much…

Tim