2. Let A be an (m x n)-matrix and B an (n xt)-matrix over R. (a) Show that row(AB) C row(B). Further, if A is invertible (m = n), then row(AB): = row(B). (b) Show that rank(AB)

please help with 2a and b

2. Let A be an (m x n)-matrix and B an (n xt)-matrix over R.<br>(a) Show that row(AB) C row(B).<br>Further, if A is invertible (m = n), then row(AB):<br>= row(B).<br>(b) Show that rank(AB) < rank(B).<br>Further, if A is invertible (m =n), then rank(AB) = rank(B).<br>

Extracted text: 2. Let A be an (m x n)-matrix and B an (n xt)-matrix over R. (a) Show that row(AB) C row(B). Further, if A is invertible (m = n), then row(AB): = row(B). (b) Show that rank(AB) < rank(b).="" further,="" if="" a="" is="" invertible="" (m="n)," then="" rank(ab)="">

Jun 04, 2022

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2. Let A be an (m x n)-matrix and B an (n xt)-matrix over R. (a) Show that row(AB) C row(B). Further, if A is invertible (m = n), then row(AB): = row(B). (b) Show that rank(AB)

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