SOLUTION: A is a 2x3 matrix and B a 3x2 matrix is A-B defined A is invertible 3x3 matrix B is 3x4 matrix is A to the -1 power B defined A is 3x4 matrix and B is 3x4 matrix is A+B

Question 288488: A is a 2x3 matrix and B a 3x2 matrix is A-B defined
A is invertible 3x3 matrix B is 3x4 matrix is A to the -1 power B defined
A is 3x4 matrix and B is 3x4 matrix is A+B defined
I do not understand what is meant my defined
thank you
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A is a 2x3 matrix and B a 3x2 matrix is A-B defined?
Ans: No because the dimensions are not the same.
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A is invertible 3x3 matrix B is 3x4 matrix is A to the -1 power B defined
Ans: Yes because the "inner" dimensions are the same.
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A is 3x4 matrix and B is 3x4 matrix is A+B defined?
Ans: Yes because the dimensions are the same.
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I do not understand what is meant my defined
For these problems "defined" means you can perform the operation.
"Not defined" means you cannot carry out the operation.
The operations are multiplication of addition.
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cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to add or subtract two matrices, the two matrices need to be of the same size. Since A and B are of different sizes (A is 2x3 but B is 3x2), you CANNOT subtract B from A. It doesn't make sense to subtract the two matrices if they are of different sizes. So A-B is NOT defined.

If A is a 3x3 invertible matrix, then is also a 3x3 matrix. Because has 3 columns and B has 3 rows, this means that the inner dimensions match. This means that you are able to multiply and B. So is defined.

Since A and B are of the same size, it is perfectly possible to add up the two matrices. So A+B is defined.
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