将 2x + 3y + z + 5t = 8 写成矩阵 A(有几行?)乘列向量 x = (x, y, z, t)产生 b。请问 解 x 是 4 维空间中的平面还是超平面? 平面是三维的,且没有 4D 的体积。
答案:
2x+3y+z+5t = 8 is Ax = b with the 1 by 4 matrix A = [ 2 3 1 5 ] : one row. The solutions (x, y, z, t) fill a 3D “plane” in 4 dimensions. It could be called a hyperplane.