搜搜做题作业网线性代数关于矩阵的问题,
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线性代数关于矩阵的问题,
Suppose that AX = B is the matrix representation of a system of linear
equations.
(a) Suppose that Y is a solution of this system,and that Z1 and Z2 are solutions of
the associated homogeneous system.Show that Y 17Z1 + 16Z2 is also a solution of
AX = B .
(b) Suppose that Y1 and Y2 are solutions of AX = B .Show that 2Y1 Y2 is also a
solution of AX = B .
Suppose that AX = B is the matrix representation of a system of linear
equations.
(a) Suppose that Y is a solution of this system,and that Z1 and Z2 are solutions of
the associated homogeneous system.Show that Y 17Z1 + 16Z2 is also a solution of
AX = B .
(b) Suppose that Y1 and Y2 are solutions of AX = B .Show that 2Y1 Y2 is also a
solution of AX = B .
Y后面的运算符应该是减号吧
(a) 由已知,AY=B,AZ1=0,AZ2=0
所以 A(Y-17Z1+16Z2) = AY-17AZ1+16AZ2 = B - 0 + 0 = B
所以 Y-17Z1+16Z2 也是 AX=B 的解.
(b) 由已知 AY1=B,AY2=B
所以 A(2Y1-Y2) = 2AY1-AY2 = 2B - B = B
所以 2Y1-Y2 也是 AX=B 的解.
(a) 由已知,AY=B,AZ1=0,AZ2=0
所以 A(Y-17Z1+16Z2) = AY-17AZ1+16AZ2 = B - 0 + 0 = B
所以 Y-17Z1+16Z2 也是 AX=B 的解.
(b) 由已知 AY1=B,AY2=B
所以 A(2Y1-Y2) = 2AY1-AY2 = 2B - B = B
所以 2Y1-Y2 也是 AX=B 的解.