Solving Matrix Multiplication: A*B^T with A=2,1;5,3 and B=1,-1,1;-1,1,1

In summary, the problem is to find A*B^T, where A=2 15 3and B=1 -1 1-1 1 1The transpose of B results in a 3x2 matrix, making it impossible to multiply by a 2x2 matrix. The correct solution would be (AB)^T. However, the original problem was written as B*A, making it impossible to compute. This was a simple mistake and the correct solution is (AB)^T.
  • #1
lagwagon555
60
1

Homework Statement


Find A*B^T, where A=

2 1
5 3

And B=

1 -1 1
-1 1 1


Homework Equations



n/a



The Attempt at a Solution



The problem is, is that if I get the transpose of B, I will end up with a 3x2 matrix. Isn't this impossible to multiply by a 2x2 matrix? Maybe the answers is just 'not possible', but I have a feeling I'm doing something wrong. Anybody got any pointers? Thanks!
 
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  • #2
You are right, A*BT can't be computed. (AB)T can though, are you sure you weren't supposed to calculate that?
 
  • #3
The way it was actually written was BTA, so I think it made a point of showing that it wasn't (AB)T. So I'm thinking that the answer is that it can't be computed? Thanks for the quick reply!

EDIT: ooooooooooh. Ooops. How embarassing. Of course it makes a difference when B comes first. Argh!
 

What is matrix multiplication?

Matrix multiplication is a mathematical operation that involves multiplying two matrices to result in a new matrix. It is different from regular multiplication as it follows certain rules and properties specific to matrices.

How do I solve for A*B^T with given matrices A and B?

To solve for A*B^T, you need to first transpose matrix B by switching its rows and columns. Then, multiply matrix A by the transposed matrix B to get the desired result.

What are the dimensions of the resulting matrix A*B^T?

The resulting matrix of A*B^T will have the same number of rows as matrix A and the same number of columns as matrix B. In this case, it will be a 2x2 matrix.

What are the properties of matrix multiplication?

Some properties of matrix multiplication include the fact that it is not commutative (A*B is not equal to B*A), it is associative (A*(B*C) is equal to (A*B)*C), and the product of two matrices may be a zero matrix even if neither of the original matrices are zero matrices.

Can I use a calculator to solve for A*B^T?

Yes, you can use a calculator to solve for A*B^T. However, it is important to make sure that the calculator has a matrix multiplication function and that you enter the matrices correctly.

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