matrices question

• Mar 6th 2009, 05:24 PM
smmmc
matrices question
hey need help urgent questions

A, B, C are m × n matrices. Is it true that
a) A + B = B + A
b) (A + B) + C = A + (B + C)?
• Mar 6th 2009, 05:27 PM
Prove It
Quote:

Originally Posted by smmmc
hey need help urgent questions

A, B, C are m × n matrices. Is it true that
a) A + B = B + A
b) (A + B) + C = A + (B + C)?

Yes, if the matrices are of the same dimensions, then the associative and commutative properties of addition still apply.
• Mar 6th 2009, 05:30 PM
smmmc
ok thanks how bout this one
1)A and B are both m × n matrices. Are AB and BA defined and, if so, how many rows and
columns do they have?
2)The matrices A and B are 2 × 2 matrices, and O is the zero 2 × 2 matrix. Is the following
argument correct?
‘If AB = O, and A = O, then B = O’.
• Mar 6th 2009, 05:33 PM
Prove It
Quote:

Originally Posted by smmmc
ok thanks how bout this one
A and B are both m × n matrices. Are AB and BA defined and, if so, how many rows and
columns do they have?

No they're not.

If matrix A was m x n and matrix B was n x m, they both would be.

AB would be m x m and BA would be n x n.

In general, if you have two matrices, I'll call them X and Y, they can only be multiplied together (in the form XY, not YX) if the number of columns in X and the number of rows in Y are equal. XY will have the same number of rows as X and the same number of columns as Y.