Multiplying 3 Matrices?

Question

Matrix A Looks This:
-1 4 -2 0
3 3 1 -4
0 5 2 -1

Matrix B Looks Like This:
1 2 5
-3 4 0
2 3 -4
-1 2 2

Matrix C Looks Like This:
-2
4
3

I know how to multiply Matrix A by Matrix B, But I don't know how to multiply anything by Matrix C.
Is it a trick question? Or do you insert 0's for the missing elements in Matrix C.

Answer 1

No you do not insert 0's for the missing elements.

in order to be able to multiply 2 matrices the number of columns of the first matrix must equal the number of rows of the second matrix.

that is, in your case

matrix A is a (3X4) matrix, 3 rows 4 columns
matrix B is a (4X3) matrix, 4 rows 3 columns

so AB = (3X4)(4X3)

since the 'inner' dimensions match we can perform the multiplication.

it turns out that the result of the multiplication is the 'outer' dimensions, that is AB will be a 3X3 matrix

lastly, since C is a (3X1) matrix

we can multiply the earlier result as (3X3)(3X1), the result will be a 3X1 matrix.

Note that we could not multiply it as (3X1)(3X3) because the 'inner' dimensions don't match.

Answer 2

I agree with polar...
after multiplying AB, you get a 3X3 matrix which you can multiply the product of AB by C since C is a 3X1 matrix
(remember: the first matrix should have the same number of rows as the columns in the second matrix)

Multiplying the product of AB by C will result in a 3X1 matrix.
Hope that helps. :)

Answer 3

I assume you want to get the matrix (AB)C.
After multiplying AB you get a 3 x 3 matrix. With this you can multiply C, which is 3 x 1.