矩阵的逆与线性方程组的解 ax1+a2x2+…+a1nxn=b a2xazx2+..+a2nxn b2 all 012 din d21 d22 d2n b2 ... anl (n2 ann or,equivalently,letting A (ai),x =(xi),and b =(bi),as Ax =b. If A is nonsingular,it possesses an inverse A-,and
矩阵的逆与线性方程组的解
逆矩阵存在的条件 A square matrix has full rank if and only if it is nonsingular. A matrix A has full column rank if and only if it does not have a null vector. A square matrix A is singular if and only if it has a null vector. An n x n matrix A is singular if and only if det(A)=0. 这是什么意思?
逆矩阵存在的条件 这是什么意思?
问题2: 如何计算非奇异矩阵的逆? 1:矩阵A的逆=A的伴随矩阵/行列式A的值 2:矩阵A的逆:对(AE)进行行初等变换得到(EA1)
1:矩阵A的逆=A的伴随矩阵/行列式A的值 2:矩阵A的逆:对(A|E)进行行初等变换得到(E|A-1 )
2 2 1 例:求3阶方阵A= 31 5 的逆矩阵。 323 解:|A|=1,M1=-7,M2=-6,M1g=3, M21=4,M2=3,M23=-2, M31=9,M2=7,M3=-4, 则 A A2 A31 An A A23 M -Ma M -7 4 -M2 Mn -M2 三 3 -7 -M3 M3 3 2 -4
123 例1设A=221,求A1. 343 123 10 0 解( AE)=22 1 0 10 3430 01 2 1 2 3 1 00 i+2 -2 -5-210 r3-3r0 -2 -6 -301 3-2