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  1. #1
    Member smmmc's Avatar
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    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)?
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  2. #2
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    Quote Originally Posted by smmmc View Post
    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.
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  3. #3
    Member smmmc's Avatar
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    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’.
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  4. #4
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    Quote Originally Posted by smmmc View Post
    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.
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