For a general matrix Xnxm with rank r min {m, n}, (1). Show that the...
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For a general matrix Xnxm with rank r ≤ min {m, n}, (1). Show that the normal equation XTXB = XTY is a consistent equa- tion for any YER", i.e. the equation always has solutions. (2). Let the zero space be Vo = {ß = Rm : XTXß = 0}, find dim (Vo). (3). The solution space is V = {ß € Rm : XTXB = X¹Y}. Is it true that dim (Vo) = dim (V)? Why? For a general matrix Xnxm with rank r ≤ min {m, n}, (1). Show that the normal equation XTXB = XTY is a consistent equa- tion for any YER", i.e. the equation always has solutions. (2). Let the zero space be Vo = {ß = Rm : XTXß = 0}, find dim (Vo). (3). The solution space is V = {ß € Rm : XTXB = X¹Y}. Is it true that dim (Vo) = dim (V)? Why?
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