- #1

nhrock3

- 415

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A , B are nXn matrices

and

AB=(A)^t

t-is transpose

prove that the space spanned by A's row equals the space spanned by A's columns

i know that there dimentions are equals

so in order to prove equality i need to prove that one is a part of the other

how to do it?

each column i of (AB)_i=A*B_i

i was told by my proff that that column i of AB is a member from the span of the columns of A

but i don't get this result

suppose the member of B_i column is (c1,c2,..,cn)

so the multiplication of A by the B_i column

we get then the first member is dot product from the first row with (c1,c2,..,cn)

i can't see how its a variation from the A columns?

and

AB=(A)^t

t-is transpose

prove that the space spanned by A's row equals the space spanned by A's columns

i know that there dimentions are equals

so in order to prove equality i need to prove that one is a part of the other

how to do it?

each column i of (AB)_i=A*B_i

i was told by my proff that that column i of AB is a member from the span of the columns of A

but i don't get this result

suppose the member of B_i column is (c1,c2,..,cn)

so the multiplication of A by the B_i column

we get then the first member is dot product from the first row with (c1,c2,..,cn)

i can't see how its a variation from the A columns?

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