theoretical computer science ( matrices )

[lynn21]

This the question.
Given. A = [1 -1
2 -2
3 -3]

And matrix B = [1
0
2]
what is the product A.B?

Ok I'm confused because the number of rows in A is 2 and number Of columns in B is 3. So the sizes of matrices do not match up. So I cannot answer the question, am I right?

[Taywin]

Maybe it is like...
Ax = B

And the question is missing something there?

[lynn21]

This the question.
Given. A = [1 -1
2 -2
3 -3]

And matrix B = [1
0
2]
what is the product A.B?

Ok I'm confused because the number of rows in A is 2 and number Of columns in B is 3. So the sizes of matrices do not match up. So I cannot answer the question, am I right?

[lynn21]

Nope nothings missing, I think its a trick question, just want to know if its possible or not to answer it.

[rubberman]

Actually matrix B has 3 rows. Actually consider it dimensionally as x, y, and z. So matrix A has 2 dimensions x (3 values), and y (2 values per dimension x), and matrix B has 1 dimension (x). So, the product matrix C is 2 dimensional. So C(X) = A(X) * B(X), and C(Y) = A(Y) * B(X).

Or more simply, using a C language structure

int A[3][2], B[3], C[3][2];
for (int i = 0; i < 3; i++)
{
   for (int j = 0; j < 2; j++)
   {
      C[i][j] = A[i][j] * B[i];
   }
}

So, matrix C should =
[ 1 -1
0 0
6 -6 ]

In any case, check out this article for a more rigorous treatment: http://en.wikipedia.org/wiki/Matrix_multiplication

[Taywin]

rubberman, that's not how you multiple 2 matrices...

Given a matrix A with m x n dimension. A matrix which can be multiply with matrix A should have n dimension. In this case, A dimension is 3 x 2 and B dimension is 1 x 3. When you multiply a matrix by hand, it should be...

Let A be  3 x 2
  |a b|
  |c d|
  |e f|
Then B could be 2 x 3 (at least m must be 2)
  |g h i|
  |j k l|

So AxB is equal (produce 3 x 3)
  |(a*g)+(b*j)  (a*h)+(b*k)  (a*i)+(b*l)|
  |(c*g)+(d*j)  (c*h)+(d*k)  (c*i)+(d*l)|
  |(e*g)+(f*j)  (e*h)+(f*k)  (e*i)+(f*l)|

Though, I can see a portion cut out from the question where xA is. Could you actually show the whole question?

[lynn21]

Ok I'm going to upload a pic now, it gives four possible answers I chose answer 4 because I think I am unable to answer the question because the sizes of the matrices do not match

[Taywin]

Yes, #4 is correct to me. It just tests you if you understand matrix multiplication.

[DavidB]

I agree too.
Answer 4 is the best.

This product cannot be calculated.

Matrix A is 3 x 2 and Matrix B is 3 x 1.
To be able to form the product AB, the number of columns of A has to be the same as the number of rows of B.

[Momerath]

2 is the correct answer. That's not multiply, that's dot product. Notice the dot between them.

[Rashakil Fol]

Unless there's some atypical definition of dot product, you can't take the dot product of two matrices, or of a matrix and a vector.