求从x1,x2,x3到z1,z2,z3的线性变换答:解: 设 Y=P1X, Z=P2Y, 则 Z=P2P1X 其中 P1 = 1 2 -1 3 4 -2 5 -4 1 P2 = 3 -1 0 -2 1 1 2 -1 4 所以 P2P1 = 0 2 -1 6 -4 1 19 -16 4 所以从x1,x2,x3到z1,z2,z3的线性变换为 z1=2x2-x3 z2=6x1-4x2+x3 z3=19x1-16x2+4x3 ...
设矩阵X,A满足关系式XA=X+A?答:设矩阵X为:X = [x1, x2, x3 x4, x5, x6 x7, x8, x9]根据题目所给的关系式,可以列出如下方程:[XA]ij = [X + A]ij 展开左侧,有:(x1+2x4, -3x1+x5, 2x4) (1,-3,0)(x2+2x5, x5, 0) [1, 2, 0] = (2, 1, 0)(x7+2x9, x8+2x9, 2x9) (0, 0, 2)将...