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數學矩數help[1題20點!]
發問:
1) {x+3y+2z=21 {3x+2y-z=21 {5x-3y+4z=21 (a) Show that z=2 (b)Hence,find x and y
最佳解答:
(a)In order to show that z=2, we have to express y,z in term of z. x+3y+2z=21－－－(1) 3x+2y-z=21－－－(2) 5x-3y+4z=21－－－(3) (1)+(3):6x+6z=42 x+z=7 x=7-z－－－(4) Sub (4) into (1):(7-z)+3y+2z=21 3y+z=14 y=(14-z)/3－－－(5) Sub (4)&(5) into (2):3(7-z)+2[(14-z)/3]-z=21 9(7-z)+2(14-z)-3z=63 63-9z+28-2z-3z=63 -14z=63-63-28=-28 i.e.z=2 (b)From(4):x=7-z=7-2=5 From(5):y=(14-2)/3=4
其他解答:
數學矩數help[1題20點!]
發問:
1) {x+3y+2z=21 {3x+2y-z=21 {5x-3y+4z=21 (a) Show that z=2 (b)Hence,find x and y
最佳解答:
(a)In order to show that z=2, we have to express y,z in term of z. x+3y+2z=21－－－(1) 3x+2y-z=21－－－(2) 5x-3y+4z=21－－－(3) (1)+(3):6x+6z=42 x+z=7 x=7-z－－－(4) Sub (4) into (1):(7-z)+3y+2z=21 3y+z=14 y=(14-z)/3－－－(5) Sub (4)&(5) into (2):3(7-z)+2[(14-z)/3]-z=21 9(7-z)+2(14-z)-3z=63 63-9z+28-2z-3z=63 -14z=63-63-28=-28 i.e.z=2 (b)From(4):x=7-z=7-2=5 From(5):y=(14-2)/3=4
其他解答:
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{x+3y+2z=21----------(1) {3x+2y-z=21-----------(2) {5x-3y+4z=21---------(3) 介紹一種2階行列式解法 (2)-(1) 2x-y-3z=0 (3)-(2) 2x-5y+5z=0 x y z x y z 2 -1 -3 2 -1 -3 2 -5 5 2 -5 5 x:y:z=(-5-15):(-6-10):(-10+2)=20:16:8=5:4:2 x=5t,y=4t,z=2t 5t+12t+2t=21 t=1 x=5,y=4,z=2
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