(d) Let A := 0 1 1 2 2 1 2 3 ,u := 2 and v := [1 22 1]. Then, u E col(A) and vg row 2. Let A be an (m x n)-matrix and B an (n x t)-matrix over R. (a) Show that row(AB) C row(B). Further, if A is...

please help with question 2a and 2b ONLY NEVER MIND THE OTHER CONTENT

(d) Let A := 0 1 1 2<br>2 1 2 3<br>,u :=<br>2 and v := [1 22 1]. Then, u E col(A) and vg row<br>2. Let A be an (m x n)-matrix and B an (n x t)-matrix over R.<br>(a) Show that row(AB) C row(B).<br>Further, if A is invertible (m = n), then row(AB) = 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: (d) Let A := 0 1 1 2 2 1 2 3 ,u := 2 and v := [1 22 1]. Then, u E col(A) and vg row 2. Let A be an (m x n)-matrix and B an (n x t)-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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(d) Let A := 0 1 1 2 2 1 2 3 ,u := 2 and v := [1 22 1]. Then, u E col(A) and vg row 2. Let A be an (m x n)-matrix and B an (n x t)-matrix over R. (a) Show that row(AB) C row(B). Further, if A is...

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